From simulated ensembles to empirical cumulative distribution functions of selected quantiles
quant2ecdf.RdComputes empirical cumulative distribution functions (ECDFs) for user-selected quantiles derived from an ensemble of simulated values, with optional weighting and plotting.
This function is especially useful in hydrology when comparing the distribution of low, median, and high simulated flows across behavioural parameter sets, for example in GLUE-style analyses, ensemble streamflow prediction, or uncertainty assessment. It helps summarise not only the central tendency of simulated quantiles, but also their full empirical distribution across acceptable model runs.
Usage
quant2ecdf(sim, ...)
# Default S3 method
quant2ecdf(sim, weights=NULL, byrow=TRUE,
quantiles.desired= c(0.05, 0.5, 0.95), plot=TRUE, obs=NULL,
quantiles.labels= c("Q5", "Q50", "Q95"), main=NULL,
ylab="Probability", col="blue", leg.cex=1.2, leg.pos="bottomright",
cex.axis=1.2, cex.main=1.2, cex.lab=1.2, verbose=TRUE, ...)
# S3 method for class 'matrix'
quant2ecdf(sim, weights=NULL, byrow=TRUE,
quantiles.desired= c(0.05, 0.5, 0.95), plot=TRUE, obs=NULL,
quantiles.labels= c("Q5", "Q50", "Q95"), main=NULL,
ylab="Probability", col="blue", leg.cex=1.2, leg.pos="bottomright",
cex.axis=1.2, cex.main=1.2, cex.lab=1.2, verbose=TRUE, ...)
# S3 method for class 'data.frame'
quant2ecdf(sim, weights=NULL, byrow=TRUE,
quantiles.desired= c(0.05, 0.5, 0.95), plot=TRUE, obs=NULL,
quantiles.labels= c("Q5", "Q50", "Q95"), main=NULL,
ylab="Probability", col="blue", leg.cex=1.2, leg.pos="bottomright",
cex.axis=1.2, cex.main=1.2, cex.lab=1.2, verbose=TRUE, ...)Arguments
- sim
A matrix or data.frame with simulated values obtained from different parameter sets, model structures, or ensemble members.
By default, each row of
simis assumed to correspond to one behavioural simulation, and the quantiles are computed across the values stored in that row. This layout is often convenient when each row represents a complete simulated time series or a set of simulated values associated with one parameter set.- weights
Optional numeric vector of weights used when constructing the ECDFs of the quantiles. In hydrological applications these weights will often represent likelihoods, goodness-of-fit measures, posterior weights, or other measures of behavioural performance assigned to each simulation.
If
weightsis omitted,NULL, or a zero-length vector, the ECDFs are unweighted.When
byrow=TRUE,length(weights)must be equal tonrow(sim)because one quantile set is computed per row.When
byrow=FALSE,length(weights)must be equal toncol(sim)because one quantile set is computed per column.- byrow
Logical value indicating whether quantiles are computed for each row or for each column of
sim.When
byrow=TRUE(the default), quantiles are computed for each row ofsim. Use this when each row stores the simulated values associated with one behavioural parameter set.When
byrow=FALSE, quantiles are computed for each column ofsim. This is often convenient when behavioural simulations are stored in columns, for example when each column is one ensemble member and rows correspond to time steps.- quantiles.desired
Numeric vector with the probabilities of the quantiles to be analysed. The default is c(0.05, 0.5, 0.95), corresponding to the 5%, 50%, and 95% quantiles.
These are commonly used in hydrology to characterise low-flow, median-flow, and high-flow behaviour, but any set of probabilities between 0 and 1 can be supplied.
- plot
Logical value indicating whether a plot of the resulting ECDFs should be produced.
- obs
Optional numeric, integer, or
zooobject with observed values. Only used whenplot=TRUE.When provided, the corresponding observed quantile is added to each panel as a vertical reference line, allowing a direct visual comparison between the simulated ECDF and the observed benchmark.
- quantiles.labels
Optional character vector with labels for
quantiles.desired. Only used whenplot=TRUE. The default is c("Q5", "Q50", "Q95").Using informative labels can improve figure readability, especially when presenting hydrological uncertainty bounds to non-specialist audiences.
- main
Optional title for the plot. Only used when
plot=TRUE.- ylab
Label for the y-axis. Only used when
plot=TRUE. Seeplot.- col
Colour used for plotting the ECDFs. Only used when
plot=TRUE. Seepar.- leg.cex
Numeric character expansion factor used in the legend. Only used when
plot=TRUE. The default is1.2.- leg.pos
Keyword indicating the legend position. Only used when
plot=TRUE. Seelegend.- cex.axis
Numeric magnification used for axis annotations relative to
cex. Only used whenplot=TRUE. Seepar.- cex.main
Numeric magnification used for the main title relative to the current
cexsetting. Only used whenplot=TRUE.- cex.lab
Numeric magnification used for x- and y-axis labels relative to the current
cexsetting. Only used whenplot=TRUE. Seepar.- verbose
Logical value indicating whether progress messages should be printed.
- ...
Further arguments passed to
plotor from other methods.
Details
The function proceeds in two steps:
For each simulation unit defined by
byrow, it computes the unweighted quantiles specified inquantiles.desiredusingwquantile.For each requested quantile level, it computes an empirical cumulative distribution function across the ensemble of previously computed quantile values using
wtd.Ecdf. Ifweightsis supplied, the ECDF is weighted accordingly.
This workflow is useful when the analyst wants to assess how uncertain a given summary of the simulations is. For example, instead of reporting only one median low-flow estimate across behavioural runs, the function allows the user to inspect the full ECDF of that low-flow quantile and compare it with the corresponding observed value.
Value
A named list with one element for each value in quantiles.desired. The element names are taken from quantiles.labels.
Each list element is the object returned by wtd.Ecdf, typically containing at least:
- x
The sorted unique values of the selected simulated quantile across the ensemble.
- ecdf
The empirical cumulative probabilities associated with
x. If the first estimated CDF value is greater than zero, an additional point at probability zero may be added at the minimum value.
If plot=TRUE, the function also produces a multi-panel figure with one ECDF per requested quantile, optionally including the corresponding observed quantile, the median of the simulated ECDF, and the percentage bias of that median relative to the observed quantile.
Author
Mauricio Zambrano-Bigiarini, mzb.devel@gmail.com
Note
This function relies on wtd.Ecdf from the Hmisc package.
Examples
#########################################################################
# Example 1: Unweighted ECDFs of selected quantiles from a streamflow
# ensemble
#########################################################################
# Simulated streamflows from 1000 behavioural parameter sets (rows)
# and 100 time steps (columns)
set.seed(123)
sim <- matrix(abs(rnorm(50 * 100, mean=20, sd=8)), nrow=1000, ncol=100)
# Unweighted ECDFs for Q5, Q50, and Q95 across behavioural simulations
q.ecdf <- quant2ecdf(sim, byrow=TRUE, plot=FALSE)
#> [ Computing un-weighted quantiles for each ROW of 'sim' ... ]
#>
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#> [ Computing the UN-weighted ECDF for quantile 0.05 , 1/3=> 33.33% ... ]
#> [ Computing the UN-weighted ECDF for quantile 0.5 , 2/3=> 66.67% ... ]
#> [ Computing the UN-weighted ECDF for quantile 0.95 , 3/3=> 100% ... ]
str(q.ecdf, max.level=1)
#> List of 3
#> $ Q5 :List of 2
#> $ Q50:List of 2
#> $ Q95:List of 2
#########################################################################
# Example 2: Weighted ECDFs using likelihood-type weights
#########################################################################
# In GLUE-type applications, each behavioural simulation can be assigned
# a weight representing its relative performance.
weights <- runif(nrow(sim))
weights <- weights / sum(weights)
q.ecdf.w <- quant2ecdf(sim, weights=weights, byrow=TRUE, plot=FALSE,
quantiles.desired=c(0.05, 0.5, 0.95),
quantiles.labels=c("Q5", "Q50", "Q95"))
#> [ Computing un-weighted quantiles for each ROW of 'sim' ... ]
#>
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#> [ Computing the weighted ECDF for quantile 0.05 , 1/3=> 33.33% ... ]
#> [ Computing the weighted ECDF for quantile 0.5 , 2/3=> 66.67% ... ]
#> [ Computing the weighted ECDF for quantile 0.95 , 3/3=> 100% ... ]
#########################################################################
# Example 3: Visual comparison against observed flows
#########################################################################
obs <- abs(rnorm(100, mean=21, sd=7))
quant2ecdf(sim, weights=weights, byrow=TRUE, obs=obs,
main="ECDFs of simulated flow quantiles")
#> [ Computing un-weighted quantiles for each ROW of 'sim' ... ]
#>
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#> [ Computing the weighted ECDF for quantile 0.05 , 1/3=> 33.33% ... ]
#> [ Computing the weighted ECDF for quantile 0.5 , 2/3=> 66.67% ... ]
#> [ Computing the weighted ECDF for quantile 0.95 , 3/3=> 100% ... ]
#> $Q5
#> $Q5$x
#> [1] 0.06334242 0.06334242 0.06533082 0.06650415 0.09178055 0.10780876
#> [7] 0.25269173 0.27281445 0.29939987 0.33544881 0.38807192 0.39474220
#> [13] 0.41102917 0.49357570 0.81359736 0.83230536 0.87620007 0.91365799
#> [19] 0.96418891 0.98074460 1.01063315 1.03460353 1.06006117 1.12173889
#> [25] 1.14519162 1.24410901 1.27735504 1.28738239 1.31242135 1.33370098
#> [31] 1.35713091 1.36597230 1.36797229 1.37312294 1.42531529 1.43388980
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#> [49] 2.02887003 2.10793387 2.18874011 2.20009843 2.27093235 2.27790092
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#> [355] 8.93893742 8.97353624 8.97946349 9.01177061 9.04679724 9.05929759
#> [361] 9.06701362 9.07179665 9.08134642 9.08770038 9.12127437 9.13536753
#> [367] 9.15245761 9.16932531 9.17678520 9.19119691 9.22776884 9.26231709
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#> [385] 9.51358773 9.59562410 9.65496440 9.68508649 9.68784421 9.69027012
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#> [397] 9.76465863 9.79370189 9.79602635 9.81309757 9.84603966 9.85248081
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#> [439] 10.41273150 10.42109198 10.42451830 10.45625185 10.45654384 10.45873116
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#> [463] 10.65526702 10.67052234 10.68928343 10.70053429 10.70172209 10.70642505
#> [469] 10.71000048 10.73266717 10.75066085 10.77108970 10.79022932 10.81783400
#> [475] 10.83541674 10.85346995 10.88639488 10.89041454 10.90699050 10.91529224
#> [481] 10.93232032 10.96712366 10.98319056 10.99682514 11.00273831 11.00317063
#> [487] 11.03457201 11.04080223 11.06578900 11.08139084 11.09481191 11.09752653
#> [493] 11.11420809 11.11834253 11.12661509 11.13337671 11.14764512 11.15348377
#> [499] 11.15733151 11.15853817 11.16998291 11.18611670 11.19134607 11.19386990
#> [505] 11.19862225 11.20359247 11.23483781 11.27199779 11.28006502 11.28423661
#> [511] 11.28683847 11.29935429 11.30573715 11.31105408 11.33837991 11.37056910
#> [517] 11.37674128 11.38063478 11.38882644 11.39793618 11.40110133 11.40676357
#> [523] 11.42567019 11.42602465 11.44758556 11.45226819 11.45596106 11.45741035
#> [529] 11.49119586 11.49339093 11.51500625 11.52312318 11.52700443 11.52879263
#> [535] 11.53127571 11.55986366 11.57282392 11.57989377 11.59497056 11.60562118
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#> [553] 11.75557811 11.78863280 11.79196441 11.79366983 11.79498359 11.79566201
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#> [583] 12.08374238 12.08493940 12.09245662 12.10930946 12.11568710 12.11719799
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#> [601] 12.25619606 12.25730381 12.25957804 12.30257384 12.30514693 12.30564779
#> [607] 12.32535797 12.33146026 12.33720486 12.34263623 12.38119111 12.41171952
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#> [619] 12.48883264 12.50744773 12.52579284 12.54137929 12.56774008 12.57722705
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#> [631] 12.69595575 12.70514781 12.73652241 12.74896804 12.76627980 12.79644245
#> [637] 12.81583037 12.81659373 12.83241742 12.83693563 12.83709314 12.83865610
#> [643] 12.86708971 12.88572482 12.90825591 12.91651645 12.94915150 12.95829964
#> [649] 12.97168128 12.97246515 12.99745161 12.99795618 13.00208565 13.03265829
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#> [661] 13.13825151 13.15392334 13.18257366 13.18406489 13.19648442 13.20236523
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#> [673] 13.31284757 13.35150222 13.36417911 13.37724246 13.38762219 13.39020909
#> [679] 13.42993165 13.43210642 13.46260028 13.46355714 13.46842219 13.48165773
#> [685] 13.48502179 13.52482722 13.52600851 13.54813875 13.56776009 13.57121708
#> [691] 13.59294132 13.59418341 13.60618460 13.61173634 13.67513771 13.68829426
#> [697] 13.70254017 13.71011264 13.73521923 13.74238524 13.75598713 13.76095805
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#> [709] 13.85340897 13.88315189 13.89637272 13.93508220 13.94241102 13.97848825
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#> [721] 14.10737414 14.12160598 14.13946810 14.15041603 14.17149901 14.21077429
#> [727] 14.25227023 14.25677518 14.26225471 14.28210777 14.29449743 14.31359764
#> [733] 14.31674749 14.32639390 14.34942806 14.35681327 14.36687730 14.37066186
#> [739] 14.37878688 14.38231490 14.40030497 14.45356378 14.46027884 14.49593107
#> [745] 14.50547478 14.50699193 14.55450057 14.55763855 14.58583576 14.60115255
#> [751] 14.65705726 14.66158284 14.66635992 14.67886822 14.69914179 14.70707412
#> [757] 14.73054515 14.74507026 14.74605660 14.75329521 14.75709416 14.75786288
#> [763] 14.76431576 14.76976140 14.77780483 14.79091980 14.81360563 14.82396454
#> [769] 14.83908835 14.83930744 14.85146090 14.85168853 14.85444167 14.86020947
#> [775] 14.88213570 14.88304136 14.90650896 14.90981205 14.92201388 14.94972040
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#> [913] 17.47047228 17.51783228 17.55229869 17.57689561 17.59644377 17.60190003
#> [919] 17.60626942 17.61133692 17.67545691 17.68781384 17.70587839 17.70686823
#> [925] 17.72789935 17.75407956 17.75458976 17.79280626 17.79287620 17.82354185
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#> [967] 19.51342436 19.53309488 19.56777500 19.73873238 19.81180409 19.82564368
#> [973] 19.91921862 20.11763755 20.17544850 20.27622137 20.30161444 20.37386822
#> [979] 20.52123146 20.66417726 20.70944903 20.85198218 20.85788028 21.06995708
#> [985] 21.38127347 21.48427649 21.49640917 21.64448967 21.64504049 21.67828712
#> [991] 21.72363795 21.82091952 22.06221986 22.25455449 22.64671377 23.69252875
#> [997] 23.71036913 24.15525763 24.22829960 25.48908204 27.64292512
#>
#> $Q5$ecdf
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#> [235] 0.231229140 0.231416503 0.233045421 0.234695709 0.235774970 0.237212637
#> [241] 0.238121898 0.239004176 0.239541584 0.240724419 0.242395130 0.243835036
#> [247] 0.244688924 0.246417000 0.246642717 0.247339787 0.248932688 0.249549441
#> [253] 0.250472078 0.251582424 0.251697464 0.253647089 0.254244501 0.255789423
#> [259] 0.256319065 0.256560440 0.257781442 0.259653679 0.260866862 0.262012533
#> [265] 0.263034881 0.264238312 0.264425235 0.266344743 0.267976268 0.267995401
#> [271] 0.268994283 0.269761404 0.271726628 0.272297222 0.273221318 0.274823191
#> [277] 0.275479081 0.276672795 0.277412353 0.277830528 0.278842135 0.279122425
#> [283] 0.280158023 0.282041750 0.282262875 0.283999181 0.285807519 0.287183616
#> [289] 0.287342783 0.288749846 0.288751928 0.290411556 0.290998291 0.291142692
#> [295] 0.292663848 0.294332065 0.295015918 0.295299002 0.297112193 0.298466177
#> [301] 0.298981978 0.299569753 0.301213475 0.301950533 0.302232080 0.302451208
#> [307] 0.304079202 0.304211105 0.305851467 0.306105072 0.307158729 0.308206745
#> [313] 0.309883743 0.311401074 0.312008215 0.313452663 0.314266013 0.314868367
#> [319] 0.315864727 0.316365595 0.316672914 0.318405510 0.319479019 0.320528173
#> [325] 0.322104730 0.324030803 0.325124807 0.326220173 0.327333689 0.327735442
#> [331] 0.327940470 0.328321374 0.329213530 0.330370985 0.332017255 0.332794562
#> [337] 0.333229244 0.334598986 0.335701286 0.336557839 0.336668837 0.338563758
#> [343] 0.339573759 0.339976377 0.339989577 0.340595559 0.340895217 0.341464465
#> [349] 0.341828341 0.343279395 0.344514663 0.344633482 0.345199298 0.345231204
#> [355] 0.346543881 0.348199015 0.348436616 0.348928080 0.349085161 0.350390458
#> [361] 0.351559077 0.352939340 0.354579134 0.356508826 0.358241220 0.360089360
#> [367] 0.361637309 0.363170687 0.363610637 0.364624574 0.366322902 0.366942656
#> [373] 0.368912695 0.370283023 0.370816631 0.371490375 0.372919239 0.373413525
#> [379] 0.374520257 0.375391808 0.375974784 0.377313413 0.377572596 0.379392425
#> [385] 0.380710249 0.381685911 0.382650494 0.383193722 0.384226592 0.385685981
#> [391] 0.387130558 0.387538559 0.388192918 0.388875924 0.389785363 0.390189982
#> [397] 0.391592708 0.393216690 0.394823923 0.395100667 0.396413938 0.397894884
#> [403] 0.398029285 0.399771684 0.399812354 0.400768280 0.402496825 0.403671032
#> [409] 0.405032941 0.406758352 0.408261226 0.409995033 0.411798348 0.412876987
#> [415] 0.414190894 0.414476211 0.415910956 0.417542065 0.417884528 0.419196508
#> [421] 0.419382191 0.421049230 0.422426382 0.424279563 0.424631146 0.425704845
#> [427] 0.426051903 0.426709025 0.427842584 0.428153109 0.429965044 0.430753208
#> [433] 0.432337844 0.433287637 0.434611138 0.435308801 0.436836502 0.438400601
#> [439] 0.439549184 0.441521029 0.442766264 0.444399240 0.446249594 0.447397861
#> [445] 0.448514649 0.448704826 0.450292492 0.450983274 0.452498273 0.453106419
#> [451] 0.453913590 0.454638013 0.455991814 0.456947252 0.458587661 0.460352937
#> [457] 0.461084781 0.461736650 0.463403682 0.464484285 0.465091103 0.465923520
#> [463] 0.467163703 0.468804214 0.469034050 0.470112146 0.470272022 0.471278336
#> [469] 0.472931533 0.473007431 0.474444113 0.474668158 0.475462730 0.476540180
#> [475] 0.477814606 0.478284062 0.479181620 0.479260153 0.479479062 0.481190584
#> [481] 0.482658667 0.483228232 0.485039035 0.485373685 0.487357448 0.488242171
#> [487] 0.489033858 0.490704816 0.491793292 0.491991558 0.493928822 0.493965046
#> [493] 0.494139142 0.494617297 0.496260332 0.498027677 0.499003867 0.499753872
#> [499] 0.500847229 0.501927282 0.502104019 0.503661499 0.503976495 0.504958898
#> [505] 0.505961802 0.506774682 0.507714704 0.508190702 0.509586827 0.510965414
#> [511] 0.511974843 0.512143981 0.512658129 0.514364786 0.514659967 0.515315896
#> [517] 0.516658312 0.517633305 0.518198349 0.520092898 0.521809129 0.521864803
#> [523] 0.522938058 0.524082644 0.526013183 0.526140322 0.526576892 0.527120363
#> [529] 0.527733439 0.529158259 0.531127030 0.533076924 0.534704322 0.535136603
#> [535] 0.536604321 0.538547177 0.539442547 0.541359821 0.542247656 0.543040243
#> [541] 0.544572509 0.546224770 0.548147671 0.549980631 0.550213658 0.550583540
#> [547] 0.551229630 0.552660239 0.553270981 0.555222082 0.557131001 0.558510726
#> [553] 0.559670054 0.561019664 0.562796084 0.563788963 0.565571878 0.566254312
#> [559] 0.567157066 0.568686540 0.569062064 0.571021986 0.571849772 0.572260739
#> [565] 0.573523190 0.574114650 0.574691063 0.576489359 0.577225667 0.577567092
#> [571] 0.578119965 0.579648701 0.580467937 0.581075515 0.582025863 0.582519572
#> [577] 0.583395599 0.584013959 0.584745173 0.586004326 0.587041866 0.588099725
#> [583] 0.588935384 0.589208029 0.590761255 0.592483844 0.593472939 0.593962086
#> [589] 0.594274809 0.594944246 0.596764384 0.597330771 0.599093474 0.600300792
#> [595] 0.601882820 0.601884240 0.603062160 0.604243161 0.604557903 0.606036835
#> [601] 0.607661832 0.609494211 0.611397554 0.612386238 0.614324009 0.616047019
#> [607] 0.617718617 0.619638294 0.619728646 0.620619574 0.622548647 0.622729580
#> [613] 0.624516014 0.625866568 0.626557676 0.627474623 0.629208121 0.631172910
#> [619] 0.631421232 0.632416414 0.633527311 0.634806132 0.635601276 0.636590589
#> [625] 0.637860074 0.638243105 0.640005332 0.641745422 0.641902745 0.643829240
#> [631] 0.645091404 0.646236080 0.646628716 0.647891107 0.649101183 0.649564074
#> [637] 0.650067473 0.651254452 0.651410050 0.653379415 0.654716245 0.655464358
#> [643] 0.655596132 0.656434386 0.658104436 0.659167691 0.659975203 0.660229142
#> [649] 0.661963751 0.663905732 0.665613544 0.665960339 0.666092593 0.667841320
#> [655] 0.668799964 0.670413987 0.670731779 0.672066713 0.672624135 0.673563970
#> [661] 0.673960006 0.674677802 0.676037811 0.677121672 0.677368309 0.678602970
#> [667] 0.679990595 0.681807668 0.682677941 0.683872620 0.685010491 0.686267226
#> [673] 0.687907634 0.689261670 0.690210150 0.690755704 0.692726769 0.693845875
#> [679] 0.694824602 0.695475142 0.696237787 0.697515087 0.699030534 0.700163069
#> [685] 0.700323905 0.701473724 0.701674526 0.703094845 0.704600553 0.705271783
#> [691] 0.707145361 0.708642936 0.708884059 0.710661010 0.711541057 0.713140290
#> [697] 0.714068215 0.716036068 0.717521018 0.719406566 0.720136996 0.721043040
#> [703] 0.721988359 0.722007298 0.722127656 0.722496902 0.723169726 0.724570490
#> [709] 0.725773607 0.726149634 0.726274931 0.726572822 0.728277600 0.729895094
#> [715] 0.731184370 0.731705636 0.733319880 0.734895193 0.735596168 0.736670164
#> [721] 0.737301772 0.738031235 0.739017806 0.739619771 0.740486931 0.741334154
#> [727] 0.741952707 0.742303316 0.743509587 0.743890406 0.744524055 0.745051182
#> [733] 0.745059786 0.746325315 0.746620655 0.748209741 0.748937620 0.749146853
#> [739] 0.749546649 0.750494799 0.751234998 0.751501072 0.752026007 0.752446425
#> [745] 0.753258859 0.753825311 0.754128653 0.754521320 0.755882095 0.756249845
#> [751] 0.756294729 0.756876820 0.758291213 0.758388006 0.760275647 0.761281922
#> [757] 0.761679857 0.761838443 0.762743241 0.763929543 0.765673969 0.766568069
#> [763] 0.767984719 0.769017957 0.769862406 0.770217618 0.770846905 0.772270769
#> [769] 0.773295414 0.774067424 0.774845565 0.776290285 0.777073177 0.778369440
#> [775] 0.779937825 0.780738283 0.782278714 0.783223818 0.784009011 0.784745392
#> [781] 0.785958661 0.787713858 0.788685490 0.789823213 0.789873355 0.790108329
#> [787] 0.790938586 0.792516070 0.793043410 0.794600732 0.795309936 0.795379315
#> [793] 0.796316154 0.797746895 0.798520028 0.800334282 0.801465030 0.802082899
#> [799] 0.802380826 0.803979348 0.804409387 0.805065420 0.805744763 0.806444890
#> [805] 0.808257167 0.810064811 0.811489702 0.811578797 0.811690842 0.813603400
#> [811] 0.813637742 0.813904731 0.815432572 0.815714600 0.817151041 0.818225453
#> [817] 0.819115455 0.819397074 0.820841328 0.820884674 0.822012107 0.822663549
#> [823] 0.823163073 0.824319143 0.824848444 0.825591584 0.826409608 0.826687155
#> [829] 0.827534794 0.829160290 0.830955089 0.831027461 0.832535527 0.833965528
#> [835] 0.835410635 0.836057140 0.836475229 0.837802103 0.839447761 0.839629933
#> [841] 0.841019072 0.842005530 0.843582224 0.844173879 0.844545479 0.845099553
#> [847] 0.846654285 0.847082596 0.848995387 0.850940839 0.852523735 0.852688310
#> [853] 0.854503894 0.856192052 0.856925075 0.857872279 0.858598965 0.859532061
#> [859] 0.860386181 0.862047398 0.863562208 0.864699354 0.865792660 0.867465413
#> [865] 0.869292699 0.869898866 0.871626740 0.871992562 0.873437507 0.874321806
#> [871] 0.875721104 0.875817823 0.876411223 0.877947582 0.878914055 0.880406303
#> [877] 0.880687803 0.881380438 0.881460066 0.882279764 0.882907520 0.883028373
#> [883] 0.883383541 0.885233116 0.887118388 0.887503659 0.887723741 0.889269656
#> [889] 0.890887931 0.891796377 0.892197818 0.893158306 0.893496397 0.894817950
#> [895] 0.896477577 0.897671250 0.899316286 0.900457217 0.901839768 0.902114153
#> [901] 0.903674386 0.904621338 0.905605054 0.905964679 0.906083973 0.907492184
#> [907] 0.908319965 0.909903851 0.911495707 0.912554002 0.914247037 0.916141013
#> [913] 0.917405661 0.918130291 0.918292271 0.919682027 0.921545839 0.922109221
#> [919] 0.923381021 0.924681477 0.926053752 0.926963426 0.928043418 0.928983046
#> [925] 0.929000518 0.930358461 0.931435059 0.932562991 0.933107521 0.933572194
#> [931] 0.934610285 0.934893259 0.936674840 0.938593276 0.939102067 0.940271448
#> [937] 0.940679535 0.942429635 0.943075519 0.944539641 0.945238006 0.945295734
#> [943] 0.946648199 0.947188394 0.947565046 0.948982203 0.949633645 0.950182477
#> [949] 0.950745521 0.951278251 0.951777376 0.952957933 0.954597420 0.955581391
#> [955] 0.957554068 0.957599339 0.958402379 0.958619378 0.960513301 0.960932555
#> [961] 0.962490892 0.963478771 0.964722040 0.964808206 0.965708069 0.966061287
#> [967] 0.967759916 0.969726169 0.971078437 0.972355145 0.973161839 0.973792802
#> [973] 0.974077684 0.974656763 0.974923329 0.975613715 0.977362567 0.978149951
#> [979] 0.979497209 0.980761922 0.981100881 0.981794936 0.982291497 0.982562796
#> [985] 0.984118960 0.984210457 0.985034272 0.985567181 0.986686729 0.988586514
#> [991] 0.988671179 0.990351491 0.990946315 0.992226423 0.994111278 0.994818157
#> [997] 0.995797147 0.997621441 0.998174924 0.998538650 1.000000000
#>
#>
#> $Q50
#> $Q50$x
#> [1] 6.901667 6.901667 7.455447 7.910133 8.325565 8.470880 8.539724
#> [8] 8.583109 8.703794 8.838354 8.884132 9.463871 9.496949 9.766879
#> [15] 9.781120 9.930811 10.172443 10.220773 10.250305 10.283885 10.500955
#> [22] 10.547526 10.753605 10.927830 11.253594 11.435436 11.445983 11.489509
#> [29] 11.591414 11.650993 11.816129 11.887087 12.044520 12.062735 12.100631
#> [36] 12.136424 12.192586 12.376187 12.683223 12.771174 12.795942 12.840787
#> [43] 12.851873 12.877750 12.902288 12.995729 13.028240 13.035382 13.095966
#> [50] 13.129517 13.131606 13.189077 13.235172 13.256882 13.329251 13.383884
#> [57] 13.389493 13.405653 13.419989 13.450642 13.488379 13.554415 13.595780
#> [64] 13.610926 13.651940 13.669489 13.726848 13.735195 13.741651 13.747708
#> [71] 13.763231 13.767314 13.775551 13.789987 13.805478 13.827988 13.852664
#> [78] 13.891489 13.931260 13.972070 14.004732 14.069311 14.072651 14.092887
#> [85] 14.173974 14.174247 14.186300 14.191160 14.229277 14.266936 14.316663
#> [92] 14.363884 14.369719 14.387958 14.394420 14.412768 14.414667 14.440505
#> [99] 14.459876 14.563708 14.619706 14.626128 14.660852 14.666765 14.670884
#> [106] 14.677578 14.691621 14.709784 14.728970 14.759187 14.763451 14.777453
#> [113] 14.780765 14.816592 14.828465 14.862148 14.905856 14.948439 14.999686
#> [120] 15.003460 15.029932 15.106296 15.163894 15.183754 15.184857 15.187946
#> [127] 15.218256 15.225886 15.248080 15.274396 15.301914 15.303315 15.339770
#> [134] 15.340787 15.343023 15.343521 15.351461 15.352099 15.362785 15.380629
#> [141] 15.387049 15.396659 15.417553 15.432769 15.471125 15.480558 15.509252
#> [148] 15.525704 15.528819 15.542276 15.585004 15.598210 15.610152 15.610981
#> [155] 15.680620 15.682031 15.689527 15.715571 15.752748 15.778463 15.784517
#> [162] 15.786234 15.813267 15.816701 15.828542 15.831061 15.851074 15.856141
#> [169] 15.865924 15.905338 15.907170 15.931907 15.935807 15.941965 15.969065
#> [176] 15.977268 15.982458 16.003225 16.032648 16.040756 16.042408 16.045324
#> [183] 16.048935 16.058179 16.129755 16.156118 16.222639 16.241699 16.250432
#> [190] 16.266757 16.287915 16.290536 16.297966 16.333077 16.335855 16.354304
#> [197] 16.364657 16.368018 16.370829 16.424250 16.426102 16.431694 16.434704
#> [204] 16.440540 16.441744 16.450006 16.470694 16.484753 16.502724 16.505360
#> [211] 16.517358 16.528805 16.566101 16.590405 16.610560 16.620025 16.646142
#> [218] 16.664675 16.665139 16.685280 16.687873 16.690495 16.696470 16.706417
#> [225] 16.738777 16.767443 16.770317 16.782759 16.823756 16.874520 16.886680
#> [232] 16.889761 16.891196 16.910897 16.921611 16.923114 16.941927 16.958188
#> [239] 16.998634 17.024441 17.050525 17.051555 17.053179 17.090742 17.096163
#> [246] 17.100585 17.120142 17.123142 17.124914 17.136222 17.180374 17.183628
#> [253] 17.201966 17.202232 17.207796 17.219659 17.241784 17.243597 17.280260
#> [260] 17.284141 17.288931 17.293233 17.297558 17.313852 17.335033 17.335822
#> [267] 17.367689 17.371947 17.404087 17.434486 17.448299 17.460988 17.461118
#> [274] 17.467696 17.468673 17.479059 17.499649 17.505868 17.508204 17.542561
#> [281] 17.543411 17.543708 17.556243 17.568334 17.573504 17.583412 17.586027
#> [288] 17.592606 17.593179 17.631083 17.638738 17.639137 17.639428 17.646145
#> [295] 17.674272 17.692406 17.701274 17.713237 17.720772 17.721816 17.747006
#> [302] 17.748143 17.756837 17.772368 17.781070 17.792439 17.808301 17.878840
#> [309] 17.882195 17.896841 17.898575 17.898636 17.909384 17.929754 17.968271
#> [316] 17.972529 17.973817 18.002794 18.005979 18.026465 18.027772 18.040930
#> [323] 18.055214 18.058630 18.065675 18.078657 18.090807 18.098128 18.106528
#> [330] 18.111119 18.124293 18.132912 18.149375 18.150652 18.155123 18.158580
#> [337] 18.165962 18.179002 18.193835 18.206855 18.208231 18.224624 18.229391
#> [344] 18.233334 18.247109 18.251249 18.256201 18.273594 18.283964 18.316603
#> [351] 18.319794 18.324413 18.325008 18.342275 18.350488 18.353389 18.357606
#> [358] 18.361898 18.369148 18.376058 18.385627 18.401062 18.403048 18.421838
#> [365] 18.422593 18.426747 18.426985 18.427422 18.432886 18.470254 18.481227
#> [372] 18.488147 18.488618 18.489286 18.517342 18.523788 18.525529 18.541379
#> [379] 18.558500 18.583528 18.584453 18.594814 18.631099 18.634794 18.634883
#> [386] 18.651867 18.654696 18.655526 18.659376 18.666297 18.666433 18.688472
#> [393] 18.713613 18.728917 18.733648 18.735092 18.735754 18.774128 18.801682
#> [400] 18.836115 18.843111 18.847535 18.847610 18.877530 18.888391 18.888869
#> [407] 18.917541 18.920259 18.925216 18.942599 18.945001 18.951969 18.956625
#> [414] 18.974468 18.980746 18.985775 18.986895 18.998400 19.018921 19.019725
#> [421] 19.061674 19.078226 19.125463 19.125705 19.127361 19.133759 19.148819
#> [428] 19.153727 19.156893 19.184934 19.199068 19.202237 19.215577 19.221046
#> [435] 19.221972 19.226511 19.230694 19.236099 19.236559 19.238820 19.246817
#> [442] 19.256472 19.280198 19.288555 19.306287 19.312868 19.316498 19.323272
#> [449] 19.343305 19.378760 19.379688 19.390635 19.394999 19.424392 19.429535
#> [456] 19.442392 19.443185 19.449875 19.450918 19.472148 19.484945 19.485158
#> [463] 19.504619 19.504706 19.515119 19.519894 19.541407 19.543167 19.551552
#> [470] 19.555504 19.559824 19.563211 19.584145 19.585567 19.586254 19.605244
#> [477] 19.611453 19.619231 19.623605 19.651444 19.653178 19.660417 19.663275
#> [484] 19.665136 19.669278 19.683844 19.692346 19.696339 19.707702 19.771266
#> [491] 19.772840 19.790091 19.801147 19.823880 19.842008 19.856158 19.877537
#> [498] 19.885541 19.903574 19.904621 19.915808 19.934783 19.939978 19.976054
#> [505] 20.004827 20.009657 20.013470 20.021533 20.022848 20.046113 20.058321
#> [512] 20.076127 20.078230 20.087695 20.113782 20.155540 20.161090 20.208802
#> [519] 20.215394 20.220489 20.250757 20.251525 20.259713 20.267015 20.276409
#> [526] 20.297928 20.308274 20.313938 20.322543 20.329863 20.340106 20.357828
#> [533] 20.362543 20.364091 20.370558 20.382916 20.384425 20.400423 20.419115
#> [540] 20.419984 20.433584 20.434554 20.436441 20.439296 20.440553 20.473669
#> [547] 20.477999 20.481683 20.493492 20.503502 20.508378 20.513948 20.520544
#> [554] 20.536085 20.557370 20.558198 20.577334 20.588960 20.592042 20.596409
#> [561] 20.610115 20.618743 20.630628 20.636016 20.638991 20.697954 20.711144
#> [568] 20.713658 20.724893 20.725040 20.740504 20.750577 20.770968 20.794145
#> [575] 20.800397 20.808633 20.826903 20.841455 20.856230 20.857511 20.870073
#> [582] 20.870642 20.880073 20.881774 20.884298 20.898148 20.902654 20.917038
#> [589] 20.924257 20.933098 20.970547 20.973362 20.991948 20.995026 20.998689
#> [596] 21.007713 21.011299 21.016309 21.016515 21.034302 21.038569 21.039724
#> [603] 21.040054 21.040146 21.072309 21.093717 21.094589 21.096030 21.109837
#> [610] 21.125244 21.131956 21.134460 21.139667 21.152581 21.152837 21.159029
#> [617] 21.159650 21.168174 21.174496 21.200961 21.214659 21.264377 21.295926
#> [624] 21.318727 21.322568 21.343528 21.344523 21.367251 21.391995 21.397811
#> [631] 21.398422 21.421532 21.429910 21.432380 21.435969 21.446576 21.454778
#> [638] 21.464384 21.478115 21.510025 21.536003 21.538957 21.550168 21.556451
#> [645] 21.570224 21.570603 21.571393 21.585565 21.589442 21.614700 21.629312
#> [652] 21.659013 21.659049 21.659961 21.708848 21.715157 21.715394 21.716311
#> [659] 21.726209 21.735398 21.735491 21.757979 21.764053 21.768156 21.772374
#> [666] 21.818335 21.822351 21.844935 21.845069 21.848919 21.892764 21.909854
#> [673] 21.928367 21.934878 21.937992 21.942752 21.949499 21.963732 21.971594
#> [680] 21.986051 21.995311 21.997806 22.001983 22.004943 22.016680 22.059266
#> [687] 22.060368 22.071081 22.074759 22.082892 22.089744 22.108944 22.135346
#> [694] 22.142680 22.160477 22.176887 22.209244 22.210196 22.214980 22.233287
#> [701] 22.284717 22.291395 22.305359 22.340469 22.397162 22.405721 22.411191
#> [708] 22.412804 22.424366 22.432336 22.461814 22.462160 22.472373 22.480136
#> [715] 22.481842 22.483601 22.483846 22.496466 22.505348 22.512461 22.526304
#> [722] 22.535876 22.538655 22.547122 22.547839 22.551923 22.552442 22.560534
#> [729] 22.564123 22.584968 22.594435 22.598603 22.598884 22.633605 22.634076
#> [736] 22.651035 22.657621 22.660974 22.665640 22.668765 22.712305 22.716349
#> [743] 22.729947 22.743107 22.752048 22.768829 22.801828 22.815974 22.834318
#> [750] 22.834818 22.838435 22.844697 22.844701 22.850673 22.858556 22.870846
#> [757] 22.912917 22.928915 22.951716 22.969184 22.972452 22.982568 22.989478
#> [764] 22.997149 23.011389 23.019104 23.020139 23.025342 23.080324 23.083407
#> [771] 23.088676 23.096665 23.101027 23.102562 23.105150 23.122898 23.123259
#> [778] 23.133764 23.148531 23.155159 23.159765 23.162827 23.180869 23.186902
#> [785] 23.189376 23.220599 23.258953 23.291439 23.308309 23.314465 23.317606
#> [792] 23.325678 23.331649 23.337922 23.366891 23.368978 23.372024 23.408164
#> [799] 23.468963 23.469408 23.480058 23.481452 23.482312 23.490994 23.508374
#> [806] 23.517730 23.554296 23.575896 23.576164 23.615617 23.638154 23.659697
#> [813] 23.670525 23.684731 23.705727 23.752256 23.794226 23.799201 23.843482
#> [820] 23.862605 23.872795 23.876140 23.883316 23.887859 23.895983 23.898633
#> [827] 23.922421 23.927891 23.929170 23.930983 23.957050 23.976097 23.989264
#> [834] 24.033010 24.039462 24.069668 24.073649 24.075031 24.091766 24.111870
#> [841] 24.144959 24.199314 24.269480 24.289192 24.294848 24.333637 24.345552
#> [848] 24.413687 24.417262 24.437949 24.441632 24.457966 24.464826 24.496331
#> [855] 24.503916 24.535352 24.558187 24.558232 24.568071 24.573077 24.598983
#> [862] 24.663931 24.676910 24.693883 24.714684 24.725920 24.735568 24.798597
#> [869] 24.842965 24.852556 24.870232 24.877618 24.878594 24.896668 24.911384
#> [876] 24.921218 24.928983 24.931646 24.935942 24.943887 24.963054 24.967912
#> [883] 24.996733 25.006002 25.030425 25.037694 25.155012 25.182885 25.184031
#> [890] 25.186779 25.206227 25.207946 25.209235 25.223580 25.230585 25.277626
#> [897] 25.281481 25.284006 25.286562 25.315327 25.322304 25.331764 25.350011
#> [904] 25.365568 25.456796 25.498913 25.573030 25.573803 25.624014 25.628191
#> [911] 25.630301 25.659755 25.680882 25.763595 25.836483 25.837514 25.893484
#> [918] 25.918876 25.923788 25.948891 25.983881 26.028941 26.032430 26.074200
#> [925] 26.088820 26.208443 26.223756 26.256698 26.268763 26.280948 26.307124
#> [932] 26.380805 26.440425 26.449479 26.531136 26.603039 26.651530 26.702296
#> [939] 26.765852 26.776154 26.855384 26.950346 27.020248 27.074007 27.093992
#> [946] 27.178996 27.238071 27.269103 27.289677 27.313270 27.327936 27.336772
#> [953] 27.514719 27.682043 27.860520 27.947840 27.948031 28.204571 28.225392
#> [960] 28.248201 28.324588 28.332742 28.373031 28.433448 28.531918 28.564128
#> [967] 28.597411 28.624539 28.682367 28.730101 28.749089 28.772868 28.820522
#> [974] 28.826307 28.863960 28.872150 28.903321 28.930183 28.981234 29.223490
#> [981] 29.305716 29.644227 29.649945 29.685533 29.796482 29.877361 29.893406
#> [988] 29.960241 30.130503 30.344556 30.630198 30.856957 30.869326 30.911376
#> [995] 31.188576 31.207012 31.469940 31.902703 32.787900 33.015050 34.548947
#>
#> $Q50$ecdf
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#> [223] 0.236284273 0.236320497 0.238140325 0.239380507 0.240152518 0.240352086
#> [229] 0.242284495 0.243347749 0.244754812 0.245852455 0.246216332 0.246321588
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#> [241] 0.254913688 0.255727038 0.255758944 0.256012883 0.256744727 0.257003910
#> [247] 0.257686916 0.257821317 0.258645070 0.258797764 0.260136094 0.262073357
#> [253] 0.262094348 0.262123695 0.263857192 0.264426440 0.266024963 0.267996808
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#> [331] 0.335144056 0.335760808 0.336085481 0.336205291 0.338003588 0.338649677
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#> [343] 0.344195767 0.345713097 0.346047747 0.347693405 0.348476474 0.349268161
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#> [355] 0.356697868 0.357733466 0.358636220 0.359669090 0.359936079 0.361286633
#> [361] 0.362055961 0.362353851 0.363343164 0.364918305 0.366344211 0.368253131
#> [367] 0.369219604 0.369293524 0.370209859 0.371523766 0.373297258 0.375117395
#> [373] 0.376611987 0.377819305 0.379436799 0.381179199 0.382491179 0.383858357
#> [379] 0.385752906 0.387187651 0.387568470 0.389008377 0.389165700 0.389895163
#> [385] 0.390682013 0.392404602 0.393137625 0.393475716 0.395224443 0.397166424
#> [391] 0.397864789 0.398804244 0.398916289 0.399698426 0.401338788 0.401624104
#> [397] 0.403420732 0.404248518 0.404526065 0.406374206 0.407931528 0.408431052
#> [403] 0.408695265 0.408702862 0.409502642 0.410430567 0.411624240 0.411974849
#> [409] 0.413949384 0.414603743 0.414765999 0.415412504 0.416148885 0.417819844
#> [415] 0.418779252 0.420354565 0.421368502 0.422258504 0.424208398 0.424619365
#> [421] 0.426049974 0.427312365 0.428221804 0.428988925 0.429836147 0.430237588
#> [427] 0.431625213 0.432523166 0.434119161 0.434811796 0.435667112 0.435739484
#> [433] 0.437642827 0.439424407 0.440481605 0.442258556 0.442613724 0.444348333
#> [439] 0.445428385 0.447089603 0.448606171 0.449007924 0.449212951 0.449771770
#> [445] 0.449789242 0.450795556 0.452174143 0.452904574 0.454763350 0.456207604
#> [451] 0.457410721 0.458199432 0.459164015 0.460244618 0.461266966 0.463179757
#> [457] 0.464136259 0.464558996 0.466158229 0.467290764 0.468283642 0.468549716
#> [463] 0.470113816 0.470944073 0.471552219 0.471822556 0.473454081 0.473764606
#> [469] 0.474600265 0.476526760 0.477637106 0.479605663 0.481414002 0.482814766
#> [475] 0.483444054 0.483660557 0.485330607 0.486113499 0.486759383 0.487706335
#> [481] 0.488293071 0.489875098 0.491797999 0.493242577 0.494370509 0.494899811
#> [487] 0.495766972 0.496084764 0.496271687 0.498237213 0.498476406 0.499697408
#> [493] 0.500246753 0.501974627 0.502626069 0.504358665 0.506208240 0.507562041
#> [499] 0.509178307 0.510271613 0.510714463 0.511871919 0.512044273 0.512084943
#> [505] 0.512682355 0.514600792 0.516231901 0.517816537 0.518514199 0.520317514
#> [511] 0.520342509 0.520718033 0.521895953 0.523624029 0.525023327 0.525271650
#> [517] 0.525396947 0.525988602 0.526833051 0.527439869 0.527721897 0.528799348
#> [523] 0.529795246 0.529964384 0.531610654 0.532418166 0.533634711 0.534797240
#> [529] 0.536781004 0.538634185 0.539010213 0.540537914 0.541876543 0.542885973
#> [535] 0.543200968 0.543433994 0.544171053 0.544716607 0.545020911 0.546643333
#> [541] 0.547269875 0.548294520 0.550026914 0.550188894 0.550703142 0.550956746
#> [547] 0.552525132 0.552797777 0.553831015 0.554097582 0.554624709 0.554713804
#> [553] 0.555826033 0.557310983 0.558979199 0.559338825 0.559680251 0.559899379
#> [559] 0.560120504 0.561765541 0.562775542 0.564746606 0.564863705 0.565691486
#> [565] 0.566441491 0.567043455 0.568003943 0.568303601 0.569683325 0.570820471
#> [571] 0.571718864 0.572070448 0.572964548 0.573909867 0.575282142 0.576076714
#> [577] 0.577544432 0.579361505 0.580520833 0.581880842 0.583463738 0.584396021
#> [583] 0.584874176 0.585091174 0.586077632 0.586517880 0.587383387 0.589150733
#> [589] 0.589688141 0.590776617 0.591277484 0.593021910 0.594664945 0.595316813
#> [595] 0.597137988 0.598018035 0.598133075 0.599206774 0.599897556 0.600147816
#> [601] 0.600582498 0.601165475 0.601708946 0.603009401 0.603572445 0.604478489
#> [607] 0.604593555 0.605762174 0.606190485 0.607829122 0.608422522 0.610157104
#> [613] 0.611665169 0.613225402 0.613445484 0.614905807 0.615561840 0.615721007
#> [619] 0.617507440 0.618295605 0.618691640 0.620503917 0.621614813 0.622601384
#> [625] 0.622887408 0.623843334 0.625225885 0.626073525 0.626973389 0.628316641
#> [631] 0.628950290 0.630527774 0.630659548 0.631173796 0.632058096 0.633131351
#> [637] 0.634374621 0.635663897 0.636801620 0.638218777 0.638718177 0.640258607
#> [643] 0.641233601 0.641844343 0.642125963 0.642756926 0.644400648 0.645574855
#> [649] 0.646387736 0.647081791 0.648029941 0.649008669 0.649956922 0.651228848
#> [655] 0.651600448 0.653189534 0.655016820 0.656831074 0.658641876 0.660404104
#> [661] 0.660604905 0.661260976 0.662685868 0.663386843 0.664435997 0.665512595
#> [667] 0.666400430 0.667669914 0.668991467 0.669200701 0.669754775 0.670881837
#> [673] 0.672534952 0.672809337 0.673746176 0.675385662 0.675465290 0.677105699
#> [679] 0.677926549 0.678459279 0.679813263 0.681666199 0.682699949 0.683988055
#> [685] 0.684250160 0.685764970 0.686455356 0.687802614 0.689687885 0.690923153
#> [691] 0.692860924 0.694275318 0.696224942 0.697740390 0.697741810 0.699201199
#> [697] 0.700826695 0.702720619 0.703726894 0.705399648 0.706127526 0.707175543
#> [703] 0.707720073 0.708847505 0.710272325 0.710951668 0.711445377 0.711514756
#> [709] 0.711922757 0.712715344 0.713321511 0.713912970 0.715358077 0.715924530
#> [715] 0.716506621 0.716667457 0.716952339 0.718528895 0.719653111 0.720324342
#> [721] 0.720414693 0.720957921 0.722621117 0.724057558 0.724560957 0.726309809
#> [727] 0.727429357 0.729117515 0.730507271 0.732160454 0.733100475 0.733720229
#> [733] 0.734183121 0.734234849 0.734694281 0.735842864 0.737321796 0.738664213
#> [739] 0.739337037 0.740241835 0.741126558 0.742571278 0.743516382 0.743936801
#> [745] 0.745213509 0.746801175 0.748393031 0.748892156 0.750642256 0.752559530
#> [751] 0.753911798 0.755564995 0.756695743 0.757635579 0.759364124 0.760090810
#> [757] 0.761403486 0.761559084 0.762821248 0.764179191 0.764224074 0.764720636
#> [763] 0.764944681 0.765453472 0.766856198 0.767507640 0.767667516 0.767854880
#> [769] 0.767910554 0.768650752 0.769837567 0.770117856 0.771785699 0.772301500
#> [775] 0.772542624 0.774235658 0.775614152 0.776950982 0.778479718 0.779224229
#> [781] 0.779549965 0.780958176 0.782773759 0.783914690 0.784442030 0.786069428
#> [787] 0.787683451 0.788642095 0.789207911 0.790195790 0.792115467 0.792933490
#> [793] 0.793991785 0.794049513 0.795633400 0.796411541 0.797772317 0.797817588
#> [799] 0.798220207 0.798259208 0.799343069 0.800146109 0.800265402 0.800568744
#> [805] 0.802432555 0.802618238 0.803010905 0.804043590 0.804576499 0.806248097
#> [811] 0.806375237 0.807181931 0.807921489 0.808274707 0.808500424 0.808870306
#> [817] 0.808956471 0.810386473 0.811018081 0.812646075 0.812828247 0.814324767
#> [823] 0.816270219 0.817593719 0.818995216 0.819695344 0.820431651 0.820471012
#> [829] 0.820910963 0.822878816 0.823225611 0.824304250 0.824580993 0.826480778
#> [835] 0.827122206 0.829007062 0.830512770 0.831325203 0.833297880 0.834843795
#> [841] 0.836651439 0.837394579 0.839324271 0.839800269 0.840168019 0.841354321
#> [847] 0.842604478 0.842985383 0.843035526 0.844775616 0.846192266 0.848135122
#> [853] 0.849839901 0.850985571 0.852244715 0.852409290 0.852716610 0.853311434
#> [859] 0.853609360 0.854708932 0.855257764 0.855354483 0.855486737 0.855571401
#> [865] 0.856134784 0.857959077 0.858423750 0.859461841 0.861121468 0.862215472
#> [871] 0.863199188 0.864534122 0.866167097 0.867247090 0.868395357 0.868498155
#> [877] 0.869446635 0.870782428 0.872345223 0.873604376 0.875229373 0.876750529
#> [883] 0.877683626 0.879466522 0.881352070 0.883320841 0.884617132 0.885186697
#> [889] 0.886006395 0.886946023 0.888466110 0.889660789 0.891084653 0.892639385
#> [895] 0.893515413 0.893815049 0.894355244 0.894536177 0.894921449 0.896581076
#> [901] 0.897618616 0.898883328 0.900235793 0.901916105 0.903710904 0.904975552
#> [907] 0.906738256 0.907817517 0.908210153 0.908481452 0.908572949 0.909942230
#> [913] 0.911571147 0.913443384 0.914832523 0.915605655 0.915852293 0.916905949
#> [919] 0.917612828 0.918269951 0.918414351 0.919851033 0.921281774 0.923111545
#> [925] 0.924556489 0.925918398 0.926287644 0.928120022 0.928539277 0.928822251
#> [931] 0.929198903 0.929330806 0.929738893 0.930094104 0.931142187 0.932244487
#> [937] 0.933191691 0.934100953 0.935994928 0.937459051 0.938438041 0.939155838
#> [943] 0.941125203 0.941678686 0.943433884 0.944405515 0.946305065 0.947260504
#> [949] 0.949226756 0.949383837 0.949392440 0.950302114 0.952253214 0.952671389
#> [955] 0.953840769 0.955112569 0.956316000 0.957753667 0.958934224 0.960510918
#> [961] 0.961220122 0.962294534 0.962633493 0.963615896 0.963979621 0.964261121
#> [967] 0.965819458 0.967215583 0.967294116 0.968550143 0.969137917 0.969234711
#> [973] 0.970514818 0.972051177 0.972481216 0.974099491 0.975083463 0.975711219
#> [979] 0.976535034 0.978408612 0.979306170 0.980633044 0.981357674 0.982227947
#> [985] 0.983926576 0.984505655 0.986061818 0.986591460 0.988268458 0.988686548
#> [991] 0.989831224 0.990618608 0.990792704 0.992049439 0.993825859 0.994121041
#> [997] 0.995582391 0.996878653 0.997562507 0.998087442 1.000000000
#>
#>
#> $Q95
#> $Q95$x
#> [1] 14.51181 14.51181 15.36779 15.53370 15.81414 15.98141 16.04542 16.26340
#> [9] 16.48750 16.61702 16.62762 17.29038 17.29962 17.39085 17.39255 17.42913
#> [17] 17.52586 17.76094 18.07907 18.08770 18.08777 18.17895 18.28767 18.61239
#> [25] 18.64559 18.74608 18.93354 19.09088 19.33775 19.38703 19.39789 19.47373
#> [33] 19.62314 19.72746 19.73425 19.73571 19.73698 19.76245 19.76927 19.81733
#> [41] 19.87394 19.89962 19.96124 20.00611 20.03865 20.10496 20.15407 20.19740
#> [49] 20.29551 20.31236 20.31714 20.40052 20.44612 20.49190 20.56439 20.62369
#> [57] 20.67145 20.78233 20.84541 20.88831 20.90516 20.93968 20.94117 20.97258
#> [65] 21.02394 21.09036 21.15534 21.24151 21.25984 21.32722 21.48736 21.51541
#> [73] 21.53692 21.54291 21.54820 21.56532 21.57240 21.59236 21.60118 21.67663
#> [81] 21.73605 21.80703 21.83516 21.85443 21.88309 21.91378 21.91606 22.01954
#> [89] 22.03255 22.07653 22.11045 22.11209 22.18431 22.21052 22.22636 22.22699
#> [97] 22.25848 22.29471 22.31947 22.32028 22.32770 22.34677 22.38582 22.38772
#> [105] 22.41661 22.41839 22.42823 22.50583 22.57523 22.61122 22.65148 22.66755
#> [113] 22.66937 22.68681 22.68945 22.88760 22.98404 23.02768 23.03637 23.05141
#> [121] 23.05273 23.05844 23.08124 23.10692 23.11465 23.15852 23.16237 23.17615
#> [129] 23.20705 23.20723 23.21737 23.22632 23.24616 23.26357 23.28220 23.29081
#> [137] 23.30216 23.30225 23.34259 23.35666 23.37508 23.38916 23.39840 23.40811
#> [145] 23.41171 23.42221 23.42533 23.44228 23.44879 23.53034 23.60302 23.61203
#> [153] 23.63662 23.64644 23.64773 23.68803 23.68954 23.71033 23.71240 23.71974
#> [161] 23.73333 23.74681 23.79799 23.80422 23.81630 23.81691 23.82693 23.84500
#> [169] 23.86894 23.88320 23.91290 23.91348 23.93107 23.98261 23.98280 23.99970
#> [177] 24.02577 24.02934 24.06788 24.08078 24.08106 24.08930 24.13490 24.14803
#> [185] 24.14947 24.19716 24.20330 24.27737 24.29995 24.31832 24.33027 24.33148
#> [193] 24.34919 24.38718 24.41019 24.41122 24.41615 24.43315 24.47859 24.49344
#> [201] 24.49519 24.49814 24.54631 24.58249 24.59450 24.59587 24.62668 24.62720
#> [209] 24.65173 24.66558 24.67664 24.68578 24.68793 24.71869 24.71986 24.72281
#> [217] 24.72850 24.72953 24.74225 24.74727 24.75762 24.81752 24.85544 24.88163
#> [225] 24.88616 24.91585 24.93254 24.93570 24.94826 24.95693 24.97928 24.98324
#> [233] 24.98689 24.99350 25.00865 25.01467 25.05477 25.06369 25.06551 25.06667
#> [241] 25.06703 25.07783 25.08899 25.09256 25.10174 25.10249 25.10365 25.11485
#> [249] 25.13464 25.18011 25.18197 25.19879 25.20091 25.20267 25.21513 25.22178
#> [257] 25.23416 25.23836 25.27834 25.27922 25.29176 25.29803 25.31431 25.31656
#> [265] 25.36192 25.37483 25.40170 25.41703 25.45852 25.46235 25.46638 25.46725
#> [273] 25.46779 25.50912 25.53095 25.53678 25.56132 25.61085 25.61562 25.61608
#> [281] 25.64268 25.65896 25.66071 25.69282 25.69816 25.70163 25.70274 25.71520
#> [289] 25.71879 25.73065 25.74720 25.76157 25.76584 25.79611 25.79741 25.80861
#> [297] 25.81251 25.84491 25.86058 25.86992 25.87279 25.87567 25.87610 25.89067
#> [305] 25.89197 25.92720 25.93022 25.93201 25.93906 26.00849 26.05809 26.07633
#> [313] 26.07662 26.09312 26.10121 26.12020 26.12930 26.15882 26.21197 26.22485
#> [321] 26.29632 26.30191 26.30723 26.31568 26.31854 26.32297 26.32308 26.33258
#> [329] 26.33648 26.37904 26.39932 26.43226 26.44887 26.45487 26.50183 26.50623
#> [337] 26.50720 26.55986 26.57205 26.58893 26.60031 26.60061 26.60120 26.61431
#> [345] 26.62282 26.62771 26.67276 26.70989 26.71358 26.73480 26.77017 26.77046
#> [353] 26.78274 26.79757 26.79845 26.80032 26.80688 26.80712 26.82069 26.84162
#> [361] 26.85428 26.85958 26.88711 26.90980 26.91774 26.92624 26.93093 26.94672
#> [369] 26.94798 26.95753 26.96983 26.97572 26.97916 26.98108 26.98345 26.98935
#> [377] 27.00877 27.01145 27.02507 27.02600 27.04219 27.05972 27.06402 27.10459
#> [385] 27.11600 27.16101 27.16565 27.18717 27.18840 27.19483 27.20617 27.22369
#> [393] 27.23548 27.26041 27.26073 27.27411 27.28392 27.29113 27.30794 27.31802
#> [401] 27.31972 27.32488 27.33612 27.35197 27.37814 27.37841 27.40409 27.40437
#> [409] 27.42007 27.42624 27.42826 27.44783 27.48272 27.48483 27.52248 27.52419
#> [417] 27.52933 27.54580 27.56325 27.57785 27.57860 27.58527 27.61114 27.61512
#> [425] 27.62045 27.63975 27.64864 27.65731 27.69544 27.74237 27.74287 27.75548
#> [433] 27.77321 27.77615 27.79565 27.81579 27.82582 27.83218 27.84303 27.85690
#> [441] 27.88927 27.91246 27.91762 27.91977 27.92210 27.93444 27.94327 27.95360
#> [449] 27.97361 27.98287 27.98632 28.04591 28.06074 28.06173 28.06420 28.07597
#> [457] 28.09029 28.09656 28.10258 28.11641 28.11955 28.13799 28.15006 28.15206
#> [465] 28.16202 28.17843 28.18561 28.19580 28.19739 28.20336 28.25538 28.25702
#> [473] 28.27000 28.29002 28.29122 28.29238 28.31271 28.38290 28.41361 28.42169
#> [481] 28.43458 28.48773 28.48876 28.51975 28.53708 28.54429 28.59281 28.59956
#> [489] 28.60991 28.62029 28.64640 28.67694 28.67820 28.68103 28.69170 28.69314
#> [497] 28.69763 28.70937 28.71354 28.72621 28.72748 28.74378 28.74784 28.75815
#> [505] 28.76196 28.77050 28.77329 28.77471 28.83240 28.84505 28.84907 28.85575
#> [513] 28.86178 28.87766 28.87879 28.87936 28.88003 28.88569 28.89104 28.90690
#> [521] 28.91719 28.92370 28.96284 28.96455 28.96818 29.00002 29.00058 29.00534
#> [529] 29.02162 29.03316 29.03770 29.04844 29.05070 29.06040 29.10216 29.12072
#> [537] 29.12285 29.15212 29.15213 29.15313 29.15407 29.15410 29.17008 29.19046
#> [545] 29.21092 29.22569 29.24526 29.25064 29.26018 29.26328 29.29031 29.30447
#> [553] 29.31029 29.32203 29.33451 29.34707 29.34791 29.35299 29.35724 29.42068
#> [561] 29.43304 29.44604 29.44945 29.45294 29.46997 29.48660 29.52249 29.53281
#> [569] 29.56165 29.57662 29.58301 29.59061 29.60338 29.60916 29.64302 29.64957
#> [577] 29.66370 29.68736 29.71452 29.71605 29.71671 29.74487 29.75382 29.76771
#> [585] 29.77213 29.77747 29.79508 29.81268 29.84025 29.85363 29.85981 29.88555
#> [593] 29.88887 29.89340 29.94142 29.94399 29.94966 29.97139 29.99932 30.00124
#> [601] 30.01484 30.02199 30.03052 30.03965 30.08828 30.10209 30.10548 30.11597
#> [609] 30.17813 30.18372 30.20482 30.21263 30.21281 30.21322 30.22764 30.23258
#> [617] 30.25029 30.27166 30.27841 30.28167 30.32807 30.33501 30.34394 30.35267
#> [625] 30.35838 30.35957 30.36341 30.39240 30.39711 30.40159 30.41098 30.44103
#> [633] 30.47392 30.49930 30.53316 30.53328 30.53514 30.54268 30.56855 30.59534
#> [641] 30.60318 30.60727 30.62572 30.65632 30.67507 30.68589 30.73053 30.73312
#> [649] 30.74099 30.76144 30.78833 30.79794 30.80535 30.85469 30.88522 30.91738
#> [657] 30.95250 30.95280 30.96545 30.98442 30.98493 30.98853 31.00220 31.00353
#> [665] 31.02141 31.02856 31.03004 31.04412 31.04414 31.04880 31.07378 31.12355
#> [673] 31.15140 31.15731 31.16251 31.19661 31.19827 31.20355 31.22314 31.23240
#> [681] 31.23352 31.23747 31.28191 31.32221 31.36460 31.36653 31.42016 31.45405
#> [689] 31.46406 31.46540 31.48623 31.52696 31.53169 31.55641 31.55966 31.58291
#> [697] 31.60102 31.60829 31.61025 31.62254 31.62993 31.63120 31.67086 31.67973
#> [705] 31.69140 31.73387 31.75064 31.75850 31.81764 31.81944 31.82668 31.82726
#> [713] 31.83046 31.85547 31.85762 31.85922 31.86961 31.87024 31.87225 31.87470
#> [721] 31.87781 31.89622 31.90577 31.94377 31.94548 31.96849 31.97457 31.98408
#> [729] 32.02736 32.03120 32.05299 32.09916 32.11007 32.13176 32.13192 32.15374
#> [737] 32.19314 32.23906 32.26089 32.29716 32.29862 32.30589 32.30691 32.30744
#> [745] 32.32416 32.37287 32.38065 32.39443 32.46967 32.51790 32.54173 32.55864
#> [753] 32.57078 32.60246 32.62282 32.64345 32.65574 32.65749 32.66543 32.69004
#> [761] 32.69963 32.71575 32.74696 32.75291 32.75909 32.76235 32.78807 32.81251
#> [769] 32.82545 32.82816 32.83370 32.89665 32.91582 32.93261 32.93262 32.94905
#> [777] 32.96840 32.98128 32.98308 32.98897 32.98927 32.99184 32.99575 33.01390
#> [785] 33.02734 33.04054 33.06855 33.07192 33.07712 33.09491 33.11242 33.13428
#> [793] 33.20726 33.21463 33.21532 33.22838 33.24141 33.26189 33.29219 33.35336
#> [801] 33.36844 33.37095 33.40312 33.40458 33.40558 33.42503 33.47549 33.47687
#> [809] 33.50072 33.52086 33.62659 33.63045 33.66714 33.68112 33.69814 33.69844
#> [817] 33.71359 33.71515 33.71810 33.73188 33.75233 33.75594 33.79410 33.81607
#> [825] 33.85791 33.85806 33.90907 33.90994 33.96548 33.98156 33.99398 34.00905
#> [833] 34.01406 34.09810 34.11637 34.15923 34.18591 34.23231 34.23602 34.26645
#> [841] 34.29531 34.32213 34.32339 34.37369 34.45431 34.57751 34.62824 34.66126
#> [849] 34.67325 34.69750 34.70422 34.71037 34.74613 34.74916 34.75090 34.80457
#> [857] 34.86257 34.87929 34.93481 34.94924 34.95207 34.96127 34.97865 35.02291
#> [865] 35.06272 35.13609 35.16478 35.20109 35.21768 35.21889 35.24035 35.27283
#> [873] 35.34864 35.36967 35.37289 35.47057 35.51805 35.54628 35.56270 35.56681
#> [881] 35.57294 35.60577 35.62934 35.64235 35.67251 35.72998 35.75707 35.78163
#> [889] 35.78822 35.80335 35.85768 35.88089 35.89719 35.91395 35.93442 35.94594
#> [897] 35.97771 35.97931 36.01986 36.04459 36.06592 36.18236 36.21035 36.22339
#> [905] 36.27723 36.29037 36.30059 36.33564 36.34587 36.34803 36.36815 36.40068
#> [913] 36.43809 36.46801 36.51763 36.61523 36.69374 36.80087 36.85247 37.00841
#> [921] 37.01771 37.02762 37.07404 37.22987 37.25182 37.25224 37.29133 37.32530
#> [929] 37.35165 37.35621 37.47339 37.49866 37.54872 37.60608 37.64261 37.67820
#> [937] 37.71572 37.85416 37.85598 37.88482 38.18778 38.22563 38.25574 38.27293
#> [945] 38.34463 38.39695 38.44050 38.56688 38.58501 38.70023 38.92044 38.99788
#> [953] 39.04331 39.06341 39.14868 39.17962 39.30907 39.32045 39.32966 39.33419
#> [961] 39.39591 39.44181 39.66448 39.67193 39.80485 39.82997 39.86484 39.90398
#> [969] 40.01412 40.17918 40.32295 40.34324 40.42421 40.51527 40.57167 40.60360
#> [977] 40.61814 40.62354 40.78792 40.79593 41.22993 41.47887 41.53371 41.67168
#> [985] 41.88167 42.37913 42.52867 42.65781 43.15884 43.39059 43.77268 43.93220
#> [993] 44.17683 45.47236 45.88434 45.92832 46.17426 46.32414 47.12297 47.36876
#> [1001] 47.56794
#>
#> $Q95$ecdf
#> [1] 0.0000000000 0.0006130764 0.0010904654 0.0017321966 0.0019697977
#> [6] 0.0036740867 0.0051186447 0.0056101088 0.0062838531 0.0076395458
#> [11] 0.0076435940 0.0081964671 0.0093901818 0.0103658442 0.0107942254
#> [16] 0.0114912956 0.0121369844 0.0140207118 0.0159579755 0.0167783475
#> [21] 0.0175409923 0.0177392580 0.0190545282 0.0191865432 0.0210972204
#> [26] 0.0221693890 0.0241346130 0.0254478838 0.0268019191 0.0271227951
#> [31] 0.0272813814 0.0289267346 0.0291995383 0.0300904666 0.0311639754
#> [36] 0.0314470590 0.0331537159 0.0341525980 0.0341888218 0.0344805679
#> [41] 0.0345858246 0.0355273343 0.0371776222 0.0372119644 0.0383455228
#> [46] 0.0387074831 0.0387368301 0.0406673689 0.0422714502 0.0430032943
#> [51] 0.0432572331 0.0441569265 0.0443564948 0.0452280454 0.0454419266
#> [56] 0.0467207476 0.0482153401 0.0493714097 0.0497712055 0.0499839007
#> [61] 0.0514519838 0.0520283962 0.0528112885 0.0547685285 0.0547816223
#> [66] 0.0554968685 0.0555500874 0.0572616093 0.0582732167 0.0596935359
#> [71] 0.0611857836 0.0617508271 0.0633911889 0.0648276632 0.0664799237
#> [76] 0.0675866554 0.0682050148 0.0700388828 0.0714555867 0.0727734107
#> [81] 0.0735926463 0.0752330554 0.0761995287 0.0771493226 0.0783625914
#> [86] 0.0790533740 0.0804978214 0.0813772237 0.0824907401 0.0830841403
#> [91] 0.0848035382 0.0849238956 0.0858138978 0.0865509560 0.0869025396
#> [96] 0.0885430513 0.0902137621 0.0921402571 0.0936023089 0.0947126543
#> [101] 0.0947147367 0.0963132595 0.0971370134 0.0981261089 0.1000388999
#> [106] 0.1017752052 0.1020604278 0.1029525829 0.1048903542 0.1055196417
#> [111] 0.1058175318 0.1063145504 0.1073724097 0.1083227578 0.1098802380
#> [116] 0.1106623750 0.1114621555 0.1119555694 0.1134747546 0.1149776288
#> [121] 0.1159422117 0.1173566052 0.1180024886 0.1197469144 0.1198265421
#> [126] 0.1211038425 0.1226014177 0.1241890839 0.1256401374 0.1271482032
#> [131] 0.1277187966 0.1290990593 0.1304693878 0.1319972295 0.1329865423
#> [136] 0.1332215154 0.1336261347 0.1344129848 0.1355545317 0.1367618496
#> [141] 0.1383067715 0.1396600063 0.1414450129 0.1417564803 0.1430017154
#> [146] 0.1449246165 0.1458340552 0.1467945431 0.1468704416 0.1482984093
#> [151] 0.1496037062 0.1499588737 0.1515340149 0.1526146179 0.1542544122
#> [156] 0.1547871425 0.1554385844 0.1570458176 0.1588541564 0.1589691964
#> [161] 0.1596251245 0.1596327212 0.1600692911 0.1602785245 0.1622470824
#> [166] 0.1626129050 0.1635112987 0.1644900264 0.1654202375 0.1667626538
#> [171] 0.1674456597 0.1678052853 0.1694012802 0.1700477848 0.1706996531
#> [176] 0.1725584298 0.1737202986 0.1755734799 0.1759752330 0.1761917359
#> [181] 0.1764400588 0.1775772159 0.1790366051 0.1792267819 0.1801494196
#> [186] 0.1814498753 0.1825875980 0.1828724800 0.1828916132 0.1837296735
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#> [201] 0.1927538511 0.1944984516 0.1947710969 0.1958981596 0.1965041416
#> [206] 0.1974803315 0.1975013220 0.1977135537 0.1983242963 0.1994164858
#> [211] 0.1995315521 0.2010370537 0.2015641806 0.2032987621 0.2036137574
#> [216] 0.2037481582 0.2052270902 0.2055087097 0.2060627839 0.2066121295
#> [221] 0.2085382031 0.2094380668 0.2113565030 0.2128719502 0.2137960466
#> [226] 0.2145631673 0.2151499029 0.2155726407 0.2171501248 0.2188382827
#> [231] 0.2207723640 0.2222166180 0.2235688859 0.2252145437 0.2265916954
#> [236] 0.2271505145 0.2285035023 0.2303166935 0.2315103660 0.2331819645
#> [241] 0.2337839292 0.2355163231 0.2360197222 0.2368852300 0.2371522184
#> [246] 0.2387287748 0.2389128877 0.2407284710 0.2418452588 0.2421923169
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#> [261] 0.2486899700 0.2493612003 0.2495812822 0.2511345084 0.2521677466
#> [266] 0.2537696201 0.2538086210 0.2540889103 0.2546553629 0.2559939922
#> [271] 0.2567234554 0.2578732748 0.2585709374 0.2596446358 0.2609566156
#> [276] 0.2612378583 0.2627544265 0.2634823052 0.2640255330 0.2642444416
#> [281] 0.2648525881 0.2655466434 0.2673678183 0.2676381547 0.2692785635
#> [286] 0.2702744618 0.2712312080 0.2730278355 0.2738130278 0.2739721950
#> [291] 0.2740930481 0.2750209730 0.2763578032 0.2777375274 0.2780881368
#> [296] 0.2781605093 0.2800086500 0.2802752165 0.2816628411 0.2822073712
#> [301] 0.2840181735 0.2852926000 0.2869596392 0.2877952980 0.2897639525
#> [306] 0.2900459805 0.2904290119 0.2910850834 0.2920437280 0.2926101152
#> [311] 0.2938993914 0.2942526087 0.2951467085 0.2959418530 0.2972113378
#> [316] 0.2984245208 0.2988449391 0.3004912086 0.3021590514 0.3039930796
#> [321] 0.3058434332 0.3066509451 0.3080815543 0.3083765249 0.3094698821
#> [326] 0.3109910382 0.3125355588 0.3139348565 0.3149595008 0.3164652086
#> [331] 0.3169433629 0.3174062546 0.3179518091 0.3193056096 0.3199124277
#> [336] 0.3217762393 0.3221570588 0.3229642297 0.3232988799 0.3237683356
#> [341] 0.3241709541 0.3248269866 0.3250568219 0.3258013331 0.3269792528
#> [346] 0.3283265108 0.3301387876 0.3301794572 0.3315966143 0.3318358068
#> [351] 0.3333207570 0.3339375095 0.3355265957 0.3356458893 0.3372732876
#> [356] 0.3390502383 0.3392110741 0.3403241255 0.3411916829 0.3428232080
#> [361] 0.3443915937 0.3453316154 0.3470363939 0.3472009694 0.3488320790
#> [366] 0.3495304436 0.3511734785 0.3529235790 0.3537181510 0.3547956013
#> [371] 0.3563435497 0.3576784833 0.3596511597 0.3598116658 0.3617763973
#> [376] 0.3627246500 0.3640752044 0.3654518759 0.3670447766 0.3687157350
#> [381] 0.3691440462 0.3701821373 0.3716168817 0.3730196076 0.3735570155
#> [386] 0.3738697393 0.3749329936 0.3765716300 0.3769415124 0.3771186801
#> [391] 0.3788532892 0.3795237277 0.3800128742 0.3809579787 0.3827602607
#> [396] 0.3831070556 0.3843662083 0.3859912053 0.3878441415 0.3898279050
#> [401] 0.3916449780 0.3921591255 0.3930675710 0.3947961162 0.3950957530
#> [406] 0.3967352394 0.3981137335 0.3999985892 0.4010361289 0.4029306782
#> [411] 0.4035382566 0.4053701135 0.4054954107 0.4058880470 0.4062127202
#> [416] 0.4072455908 0.4075633831 0.4092084196 0.4101247553 0.4111585049
#> [421] 0.4117894678 0.4129704690 0.4138149183 0.4150551006 0.4152720991
#> [426] 0.4164931012 0.4182156895 0.4198381115 0.4200250347 0.4216096702
#> [431] 0.4221876080 0.4233562273 0.4247259687 0.4249972675 0.4262853739
#> [436] 0.4278003725 0.4286327899 0.4305183376 0.4314006157 0.4325197212
#> [441] 0.4327941059 0.4342241072 0.4347034429 0.4360757180 0.4366050200
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#> [451] 0.4430630476 0.4437454810 0.4445048350 0.4446739734 0.4448980182
#> [456] 0.4450571806 0.4465859163 0.4480107362 0.4481680594 0.4499415508
#> [461] 0.4511580956 0.4519585536 0.4529451243 0.4544043311 0.4563753956
#> [466] 0.4565071694 0.4573831966 0.4581713611 0.4585429604 0.4591328772
#> [471] 0.4597899996 0.4617096760 0.4629520491 0.4633601362 0.4637948188
#> [476] 0.4646226051 0.4660677122 0.4678165642 0.4689907716 0.4705826277
#> [481] 0.4710968763 0.4713019034 0.4724464889 0.4735264815 0.4753093974
#> [486] 0.4761019844 0.4773611278 0.4789753718 0.4804130388 0.4809532336
#> [491] 0.4820332864 0.4827696676 0.4828253413 0.4841611337 0.4856288519
#> [496] 0.4875784767 0.4893568583 0.4911766868 0.4913386669 0.4923969618
#> [501] 0.4936932525 0.4947168368 0.4947254400 0.4948853159 0.4968501048
#> [506] 0.4979477479 0.4983456820 0.4997745452 0.5010512532 0.5025451955
#> [511] 0.5034252427 0.5043846514 0.5056501813 0.5064332499 0.5077286890
#> [516] 0.5085852421 0.5101186196 0.5120275392 0.5125417872 0.5131238782
#> [521] 0.5142813337 0.5157763720 0.5159207726 0.5171075872 0.5179918869
#> [526] 0.5197256939 0.5204977041 0.5207973618 0.5211933972 0.5227762932
#> [531] 0.5233092019 0.5238087257 0.5255574525 0.5256007986 0.5263185954
#> [536] 0.5279717101 0.5291042448 0.5294734908 0.5295923099 0.5299561867
#> [541] 0.5312279862 0.5331603950 0.5351304341 0.5359512846 0.5373527816
#> [546] 0.5375337149 0.5377345162 0.5396294369 0.5404181485 0.5415114545
#> [551] 0.5427177249 0.5433442504 0.5447228376 0.5456288810 0.5471693116
#> [556] 0.5472721089 0.5486980149 0.5503707681 0.5508650549 0.5519222530
#> [561] 0.5536503293 0.5545984794 0.5548605838 0.5564860799 0.5569869474
#> [566] 0.5580383855 0.5586699937 0.5600319026 0.5608621596 0.5615349843
#> [571] 0.5632750740 0.5643721931 0.5663018853 0.5679719355 0.5687412636
#> [576] 0.5694656864 0.5700145184 0.5719744403 0.5727048710 0.5737188079
#> [581] 0.5750880883 0.5757728447 0.5764272039 0.5781670176 0.5783491900
#> [586] 0.5785047880 0.5789694608 0.5796598469 0.5808404042 0.5811257211
#> [591] 0.5829333647 0.5840114612 0.5852674880 0.5861844359 0.5862691001
#> [596] 0.5873631042 0.5893376393 0.5911649255 0.5926290478 0.5940051446
#> [601] 0.5955199547 0.5966203086 0.5971898739 0.5980023074 0.5996693393
#> [606] 0.6007967716 0.6010921112 0.6016246824 0.6029771473 0.6038049278
#> [611] 0.6041726775 0.6050203169 0.6050896961 0.6060848779 0.6076601910
#> [616] 0.6086086713 0.6101299465 0.6120810468 0.6126939072 0.6141305890
#> [621] 0.6150259591 0.6154659099 0.6166528881 0.6186207410 0.6204900318
#> [626] 0.6218572102 0.6235850839 0.6255349778 0.6266759084 0.6280339608
#> [631] 0.6297966640 0.6311105708 0.6315863032 0.6323344163 0.6328338165
#> [636] 0.6328512885 0.6345591008 0.6361753674 0.6366347995 0.6378972509
#> [641] 0.6384546730 0.6392743709 0.6404229541 0.6415351825 0.6429600739
#> [646] 0.6448453452 0.6449344404 0.6456093470 0.6462358889 0.6465219133
#> [651] 0.6472719181 0.6479645535 0.6481975799 0.6500218735 0.6500408129
#> [656] 0.6518073442 0.6536215981 0.6551799351 0.6568961665 0.6570233062
#> [661] 0.6577664462 0.6581744467 0.6593845220 0.6610085040 0.6612745786
#> [666] 0.6616003138 0.6627310619 0.6630126090 0.6639685347 0.6640202627
#> [671] 0.6652026600 0.6657856364 0.6670357934 0.6690076386 0.6699548425
#> [676] 0.6701739705 0.6718670051 0.6736967755 0.6751661727 0.6769335184
#> [681] 0.6777116601 0.6781519076 0.6791356235 0.6800921249 0.6817201191
#> [686] 0.6829553869 0.6848493628 0.6853790046 0.6860952154 0.6866164815
#> [691] 0.6876227573 0.6888660265 0.6903833569 0.6911196641 0.6913663012
#> [696] 0.6927745124 0.6947432833 0.6958889538 0.6972016301 0.6989270409
#> [701] 0.6997648688 0.7011228114 0.7012399107 0.7030347092 0.7046529844
#> [706] 0.7061806855 0.7080136463 0.7094375103 0.7099340716 0.7115107662
#> [711] 0.7121613059 0.7135045581 0.7150046440 0.7159886156 0.7166580526
#> [716] 0.7179202163 0.7181613398 0.7195779899 0.7200539884 0.7209296508
#> [721] 0.7226949265 0.7232107278 0.7242201572 0.7245274766 0.7263275020
#> [726] 0.7274470506 0.7280128666 0.7296680010 0.7308759181 0.7322814188
#> [731] 0.7323133254 0.7333062035 0.7339085583 0.7344358988 0.7354388027
#> [736] 0.7360302624 0.7371895904 0.7388665888 0.7402673529 0.7406433804
#> [741] 0.7413566313 0.7423629449 0.7427181560 0.7434954631 0.7450516266
#> [746] 0.7469806995 0.7472786256 0.7491981338 0.7509307295 0.7528969823
#> [751] 0.7545956118 0.7555746021 0.7555878021 0.7568224631 0.7577940946
#> [756] 0.7591548701 0.7605148786 0.7616631461 0.7627111624 0.7642570777
#> [761] 0.7661510010 0.7678041981 0.7681679234 0.7694641857 0.7714096373
#> [766] 0.7733091867 0.7737284410 0.7746162754 0.7763392849 0.7781716636
#> [771] 0.7792958797 0.7803797409 0.7808885324 0.7814420158 0.7830193367
#> [776] 0.7844639139 0.7847414608 0.7863253475 0.7869439003 0.7884404201
#> [781] 0.7893500940 0.7897681833 0.7900496831 0.7906568248 0.7915966604
#> [786] 0.7924638212 0.7933191368 0.7934094886 0.7944421739 0.7957690478
#> [791] 0.7958605450 0.7969628452 0.7979515298 0.7988909854 0.7990480658
#> [796] 0.7999573270 0.8006968850 0.8015671577 0.8024054121 0.8037550226
#> [801] 0.8047513822 0.8055642627 0.8065998606 0.8071632431 0.8088069652
#> [806] 0.8101285180 0.8111766011 0.8123589967 0.8130976633 0.8146604590
#> [811] 0.8166033153 0.8175401543 0.8184797823 0.8196626168 0.8203185059
#> [816] 0.8215986135 0.8219375727 0.8220987917 0.8238970884 0.8239938816
#> [821] 0.8250475385 0.8260029772 0.8272676260 0.8288039849 0.8291454108
#> [826] 0.8310330511 0.8317169050 0.8328540505 0.8348407402 0.8358832927
#> [831] 0.8376167899 0.8383177648 0.8391649875 0.8409201850 0.8425194178
#> [836] 0.8437228485 0.8447052517 0.8457845133 0.8460102303 0.8469966881
#> [841] 0.8478205030 0.8485240100 0.8496193757 0.8502708181 0.8517015594
#> [846] 0.8520396509 0.8538018781 0.8538467620 0.8558122879 0.8560890315
#> [851] 0.8561629513 0.8562130941 0.8566559440 0.8576309374 0.8592941327
#> [856] 0.8603685440 0.8607440680 0.8614509466 0.8620707006 0.8639202764
#> [861] 0.8647119632 0.8661011017 0.8677607288 0.8680559103 0.8697155375
#> [866] 0.8715891153 0.8731532143 0.8740559681 0.8746973961 0.8762174830
#> [871] 0.8780207980 0.8787609965 0.8794876824 0.8796617791 0.8805158987
#> [876] 0.8806882532 0.8814949474 0.8826643279 0.8831580369 0.8841459157
#> [881] 0.8860457009 0.8880150660 0.8889603851 0.8893713519 0.8908327022
#> [886] 0.8914275266 0.8926548816 0.8944377782 0.8955657104 0.8960993183
#> [891] 0.8965007594 0.8965460310 0.8969760699 0.8975391140 0.8977927186
#> [896] 0.8983843735 0.8989634522 0.8991491348 0.9004138470 0.9013469436
#> [901] 0.9021200763 0.9037882929 0.9053456146 0.9062925668 0.9064693041
#> [906] 0.9080513318 0.9092138618 0.9109954422 0.9120175636 0.9125610345
#> [911] 0.9141940102 0.9159804436 0.9167678276 0.9185442481 0.9192754628
#> [916] 0.9196521151 0.9215940962 0.9220263764 0.9221586303 0.9230565831
#> [921] 0.9247178002 0.9253055750 0.9263821730 0.9264788917 0.9279392151
#> [926] 0.9290387873 0.9293217613 0.9297026660 0.9304272958 0.9310334628
#> [931] 0.9326509566 0.9345842516 0.9361444844 0.9364487886 0.9371579926
#> [936] 0.9372689908 0.9377939255 0.9386401136 0.9397141095 0.9407873647
#> [941] 0.9408735299 0.9415071790 0.9427018584 0.9440979827 0.9444013240
#> [946] 0.9463138823 0.9465514050 0.9479963492 0.9493789006 0.9509929230
#> [951] 0.9526912504 0.9538359262 0.9549871927 0.9556783002 0.9561774250
#> [956] 0.9571874256 0.9573193286 0.9584078046 0.9601502043 0.9608832277
#> [961] 0.9623231340 0.9627413085 0.9643702257 0.9652677839 0.9664056552
#> [966] 0.9673104532 0.9687551728 0.9687945338 0.9698168819 0.9699366916
#> [971] 0.9701780670 0.9708574100 0.9714548223 0.9727783229 0.9746816656
#> [976] 0.9747601988 0.9761141823 0.9767320517 0.9769823112 0.9781854275
#> [981] 0.9785001697 0.9799811161 0.9810597551 0.9821089097 0.9839811468
#> [986] 0.9852378811 0.9855484068 0.9871031391 0.9887563214 0.9895743447
#> [991] 0.9903773847 0.9916493113 0.9918366749 0.9930229773 0.9936507338
#> [996] 0.9949131246 0.9956132523 0.9970496933 0.9974349645 0.9983196876
#> [1001] 1.0000000000
#>
#>