Extreme value statistics on a linear scale
Fit (via linear moments), plot (on a linear scale) and compare (by goodness of fit)
several (extreme value) distributions to estimate discharge at given return periods.
This package heavily relies on and thankfully acknowledges the package
lmomco by WH Asquith.
Open the Vignette for an introduction to the package.
The common object to share between functions is a list (
||numeric vector with (extreme) values|
||character string for main, xlab etc|
|| number between 0 and 1; upper proportion of
|| list (usually of length 17 if
||dataframe with 'Goodness of Fit' measures, sorted by RMSE of theoretical and empirical cumulated density|
|| dataframe with values of distributions for given return periods (
||Return periods according to plotting positions, see below.|
|| Colors for plotting, added in
|| Truncation percentage, only relevant for
|| Quantile estimation from
It can be printed with
distLprint, which may be transformed to a class with printing method.
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:
|| analyse extreme value statistics, calls
||plot distribution lines and plotting positions.|
|| fit the parameters, calls
||plot density or cumulated density of data and distributions.|
|| calculate goodness of fits, calls
|| compare distribution ranks of different
|| compute parametric quantile estimates. Calls
Depends on 'berryFunctions' for
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.
Berry Boessenkool, firstname.lastname@example.org, 2014-2016
If you are looking for more detailed (uncertainty) analysis, eg confidence intervals,
check out the package
extRemes, especially the function
Intro slides: http://sites.lsa.umich.edu/eva2015/wp-content/uploads/sites/44/2015/06/Intro2EVT.pdf
Parameter fitting and distribution functions: http://cran.r-project.org/package=lmomco
Distributions: https://www.rmetrics.org/files/Meielisalp2009/Presentations/Scott.pdf and: http://cran.r-project.org/web/views/Distributions.html
R in Hydrology: http://abouthydrology.blogspot.de/2012/08/r-resources-for-hydrologists.html
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