GEV: Generalized Extreme Value Distribution (for maxima) In FAdist: Distributions that are Sometimes Used in Hydrology

Description

Density, distribution function, quantile function and random generation for the generalized extreme value distribution (for maxima) with shape, scale, and location parameters equal to `shape`, `scale`, and `location`, respectively.

Usage

 ```1 2 3 4``` ```dgev(x,shape=1,scale=1,location=0,log=FALSE) pgev(q,shape=1,scale=1,location=0,lower.tail=TRUE,log.p=FALSE) qgev(p,shape=1,scale=1,location=0,lower.tail=TRUE,log.p=FALSE) rgev(n,shape=1,scale=1,location=0) ```

Arguments

 `x,q` vector of quantiles. `p` vector of probabilities. `n` number of observations. `shape` shape parameter. `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 generalized extreme value distribution, it has density
f(x) = 1/scale*(1+shape*((x-location)/scale))^(-1/shape-1)*exp(-(1+shape*((x-location)/scale))^(-1/shape))

Value

`dgev` gives the density, `pgev` gives the distribution function, `qgev` gives the quantile function, and `rgev` generates random deviates.

References

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

Examples

 ```1 2 3``` ```x <- rgev(1000,-.1,3,100) hist(x,freq=FALSE,col='gray',border='white') curve(dgev(x,-.1,3,100),add=TRUE,col='red4',lwd=2) ```

Example output

```
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FAdist documentation built on April 17, 2020, 1:24 a.m.