lmomco by WH Asquith.
Open the Vignette
for an introduction to the package. vignette("extremeStat")
dlf) with:
dat |
| numeric vector with (extreme) values |
datname |
| character string for main, xlab etc |
gofProp |
number between 0 and 1; upper proportion of dat to compute goodness of fit from |
parameter |
list (usually of length 17 if speed=TRUE) with parameters of each distribution |
gof |
| dataframe with 'Goodness of Fit' measures, sorted by RMSE of theoretical and empirical cumulated density |
returnlev |
dataframe with values of distributions for given return periods (RPs). This element is only added in distLextreme |
RP___ |
| Return periods according to plotting positions, see below. |
coldist |
Colors for plotting, added in distLplot |
truncate |
Truncation percentage, only relevant for distLquantile |
quant |
Quantile estimation from distLquantile |
distLprint, which may be transformed to a class with printing method.
PP:
Plotting positions are not used for fitting distributions, but for plotting only
The ranks of ascendingly sorted extreme values are used to compute the probability of non-exceedence Pn:
Pn_w <- Rank /(n+1) # Weibull
Pn_g <- (Rank-0.44)/(n+0.12) # Gringorton (taken from lmom:::evplot.default)
Finally: RP = Returnperiod = recurrence interval = 1/P_exceedence = 1/(1-P_nonexc.), thus:
RPweibull = 1/(1-Pn_w) and analogous for gringorton.The main functions in the extremeStat package are:
distLextreme |
analyse extreme value statistics, calls distLfit and distLextremePlot. |
distLextremePlot |
| plot distribution lines and plotting positions. |
distLfit |
fit the parameters, calls gof and distLplot. |
distLplot |
| plot density or cumulated density of data and distributions. |
distLgof |
calculate goodness of fits, calls distLgofPlot. Can also be executed with dlf to minimize computing time by not fitting the parameters again. |
distLgofPlot |
compare distribution ranks of different distLgof methods. |
distLquantile |
compute parametric quantile estimates. Calls distLfit. |
Depends on 'berryFunctions' for rmse, rsquare, logAxis, logVals.
Suggests 'pbapply' to see progress bars if you have large (n > 1e3) datasets.
At some places you will find ## not run in the examples.
These code blocks were excluded from checking while building,
mainly because they are computationally intensive and should not take so much of CRANs resources.
Normally, you should be able to run them in an interactive session.
If you do find unexecutable code, please tell me!
This package was motivated by my need to compare the fits of several distributions to data.
It was originally triggered by a flood estimation assignment we had in class 2012,
and it bothered me that we just assumed the gumbel distribution would fit the data fine.
With the updated form of the original function, I think this is a useful package to compare fits.
I am no expert on distributions, so I welcome all suggestions you might have for me.
extRemes, especially the function fevd.
https://cran.r-project.org/package=extRemes
Intro slides: http://sites.lsa.umich.edu/eva2015/wp-content/uploads/sites/44/2015/06/Intro2EVT.pdf
Parameter fitting and distribution functions: https://cran.r-project.org/package=lmomco
Distributions: https://www.rmetrics.org/files/Meielisalp2009/Presentations/Scott.pdf
and: https://cran.r-project.org/view=Distributions
R in Hydrology: http://abouthydrology.blogspot.de/2012/08/r-resources-for-hydrologists.html
data(annMax) # annual discharge maxima from a stream in Austria
plot(annMax, type="l")
dle <- distLextreme(annMax)
dle$returnlev
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