Last data update: 2014.03.03

R: Gumbel Distribution (for maxima)
 GUMBEL R Documentation

Gumbel Distribution (for maxima)

Description

Density, distribution function, quantile function and random generation for the Gumbel distribution (for maxima) with scale and location parameters equal to scale and location, respectively.

Usage

dgumbel(x,scale=1,location=0,log=FALSE)
pgumbel(q,scale=1,location=0,lower.tail=TRUE,log.p=FALSE)
qgumbel(p,scale=1,location=0,lower.tail=TRUE,log.p=FALSE)
rgumbel(n,scale=1,location=0)

Arguments

 x,q vector of quantiles. p vector of probabilities. n number of observations. scale scale parameter. location location parameter. log,log.p logical; if TRUE, probabilities p are given as log(p). lower.tail logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

Details

If X is a random variable distributed according to a Gumbel distribution, it has density
f(x) = 1/scale*exp(-(x-location)/scale-exp(-(x-location)/scale))

Value

dgumbel gives the density, pgumbel gives the distribution function, qgumbel gives the quantile function, and rgumbel generates random deviates.

References

Coles, S. (2001) An introduction to statistical modeling of extreme values. Springer

Examples

x <- rgumbel(1000,3,100)
hist(x,freq=FALSE,col='gray',border='white')

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FAdist/GUMBEL.Rd_%03d_medium.png", width=480, height=480)
> ### Name: GUMBEL
> ### Title: Gumbel Distribution (for maxima)
> ### Aliases: dgumbel pgumbel qgumbel rgumbel
> ### Keywords: distribution
>
> ### ** Examples
>
> x <- rgumbel(1000,3,100)
> hist(x,freq=FALSE,col='gray',border='white')