distLfit {extremeStat}

Fit distributions via L-moments

Description

Fit several distributions via L-moments with lmomco::lmom2par and compute goodness of fit measures.

Usage

distLfit(
  dat,
  datname = deparse(substitute(dat)),
  selection = NULL,
  speed = TRUE,
  ks = FALSE,
  truncate = 0,
  threshold = berryFunctions::quantileMean(dat, truncate),
  progbars = length(dat) > 200,
  time = TRUE,
  quiet = FALSE,
  ssquiet = quiet,
  ...
)

Arguments

dat

Vector with values

datname

Character string for main, xlab etc. DEFAULT: deparse(substitute(dat))

selection

Selection of distributions. Character vector with types as in lmom2par. Overrides speed. DEFAULT: NULL

speed

If TRUE, several distributions are omitted, for the reasons shown in lmomco::dist.list(). DEFAULT: TRUE

ks

Include ks.test results and CDF R^2 in dlf$gof? Computing is much faster when FALSE. DEFAULT: FALSE

truncate

Number between 0 and 1. POT Censored distLquantile: fit to highest values only (truncate lower proportion of x). Probabilities are adjusted accordingly. DEFAULT: 0

threshold

POT cutoff value. If you want correct percentiles, set this only via truncate, see Details of q_gpd. DEFAULT: quantileMean(x, truncate)

progbars

Show progress bars for each loop? DEFAULT: TRUE if n > 200

time

message execution time? DEFAULT: TRUE

quiet

Suppress notes? DEFAULT: FALSE

ssquiet

Suppress sample size notes? DEFAULT: quiet

...

Further arguments passed to distLweights like weightc, order=FALSE

Value

invisible dlf object, see printL.

Author(s)

Berry Boessenkool, [e-mail], Sept 2014, July 2015, Dec 2016

See Also

plotLfit, distLweights, plotLweights, extRemes::fevd, MASS::fitdistr.
More complex estimates of quality of fits: Fard, M.N.P. and Holmquist, B. (2013, Chilean Journal of Statistics): Powerful goodness-of-fit tests for the extreme value distribution. https://chjs.mat.utfsm.cl/volumes/04/01/Fard_Holmquist(2013).pdf

Examples

data(annMax)
# basic usage on real data (annual discharge maxima in Austria)
dlf <- distLfit(annMax)
str(dlf, max.lev=2)
printL(dlf)
plotLfit(dlf)

# arguments that can be passed to plotting function:
plotLfit(dlf, lty=2, col=3, nbest=17, legargs=list(lwd=3), main="booh!")
set.seed(42)
dlf_b <- distLfit(rbeta(100, 5, 2))
plotLfit(dlf_b, nbest=10, legargs=c(x="left"))
plotLfit(dlf_b, selection=c("gpa", "glo", "gev", "wak"))
plotLfit(dlf_b, selection=c("gpa", "glo", "gev", "wak"), order=TRUE)
plotLfit(dlf_b, distcols=c("orange",3:6), lty=1:3) # lty is recycled
plotLfit(dlf_b, cdf=TRUE)
plotLfit(dlf_b, cdf=TRUE, histargs=list(do.points=FALSE), sel="nor")


# logarithmic axes:
set.seed(1)
y <- 10^rnorm(300, mean=2, sd=0.3) # if you use 1e4, distLfit will be much slower
hist(y, breaks=20)
berryFunctions::logHist(y, col=8)
dlf <- distLfit(log10(y))
plotLfit(dlf, breaks=50)
plotLfit(dlf, breaks=50, log=TRUE)


# Goodness of fit: how well do the distributions fit the original data?
# measured by RMSE of cumulated distribution function and ?ecdf
# RMSE: root of average of ( errors squared )  ,   errors = line distances
dlf <- distLfit(annMax, ks=TRUE)
plotLfit(dlf, cdf=TRUE, sel=c("wak", "revgum"))
x <- sort(annMax)
segments(x0=x, y0=lmomco::plmomco(x, dlf$parameter$revgum), y1=ecdf(annMax)(x), col=2)
segments(x0=x, y0=lmomco::plmomco(x, dlf$parameter$wak), y1=ecdf(annMax)(x), col=4, lwd=2)
# weights by three different weighting schemes, see distLweights:
plotLweights(dlf)
plotLfit(distLfit(annMax              ), cdf=TRUE, nbest=17)$gof
plotLfit(distLfit(annMax, truncate=0.7), cdf=TRUE, nbest=17)$gof
pairs(dlf$gof[,-(2:5)]) # measures of goodness of fit are correlated quite well here.
dlf$gof

# Kolmogorov-Smirnov Tests for normal distribution return slightly different values:
library(lmomco)
ks.test(annMax, "pnorm", mean(annMax), sd(annMax) )$p.value
ks.test(annMax, "cdfnor", parnor(lmoms(annMax)))$p.value


# Fit all available distributions (30):
## Not run: # this takes a while...
d_all <- distLfit(annMax, speed=FALSE, progbars=TRUE) # 20 sec
printL(d_all)
plotLfit(d_all, nbest=30, distcols=grey(1:22/29), xlim=c(20,140))
plotLfit(d_all, nbest=30, ylim=c(0,0.04), xlim=c(20,140))
plotLweights(d_all)
d_all$gof

## End(Not run)