gev {evd} R Documentation

## The Generalized Extreme Value Distribution

### Description

Density function, distribution function, quantile function and random generation for the generalized extreme value (GEV) distribution with location, scale and shape parameters.

### Usage

dgev(x, loc=0, scale=1, shape=0, log = FALSE)
pgev(q, loc=0, scale=1, shape=0, lower.tail = TRUE)
qgev(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
rgev(n, loc=0, scale=1, shape=0)

### Arguments

 x, q Vector of quantiles. p Vector of probabilities. n Number of observations. loc, scale, shape Location, scale and shape parameters; the shape argument cannot be a vector (must have length one). log Logical; if TRUE, the log density is returned. lower.tail Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

### Details

The GEV distribution function with parameters loc = a, scale = b and shape = s is

G(x) = exp[-{1+s(z-a)/b}^(-1/s)]

for 1+s(z-a)/b > 0, where b > 0. If s = 0 the distribution is defined by continuity. If 1+s(z-a)/b <= 0, the value z is either greater than the upper end point (if s < 0), or less than the lower end point (if s > 0).

The parametric form of the GEV encompasses that of the Gumbel, Frechet and reversed Weibull distributions, which are obtained for s = 0, s > 0 and s < 0 respectively. It was first introduced by Jenkinson (1955).

### Value

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

### References

Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158–171.