# gev: GENERALIZED EXTREME VALUE DISTRIBUTION In Rsafd: Statistical Analysis of Financial Data in R

## Description

Density, cumulative distribution function, quantiles and random sample generation for the Generalized Extreme Value (GEV) distribution

## Usage

 ```1 2 3 4``` ``` dgev(x, m=0, lambda = 1, xi = 0) pgev(q, m=0, lambda = 1, xi = 0) qgev(p, m=0, lambda = 1, xi = 0) rgev(n, m=0, lambda = 1, xi = 0) ```

## Arguments

 `x` numeric vector. Missing values (NA's) are allowed `q` vector of quantiles. Missing values (NA's) are allowed `p` vector of probabilities. Missing values (NA's) are allowed `n` sample size. If `length(n)` is larger than 1, then `length(n)` random values are returned `Optional Arguments` `m` Location parameter. Can be a vector (see details) `lambda` Scale parameter. Can be a vector (see details) `xi` Shape parameter (note the sign convention described in `SHAPE.XI`). Can be a vector (see details)

## Details

The length of vectors `m`, `lambda`, and `xi` should either be 1 or equal to the length of the vectors `x`, `q`, `p`, or `n`. Missing values and NA's are not allowed.

## Value

Density (`dgev`), cumulative distribution function (`pgev`), quantile (`qgev`), or random sample (`rgev`) for the Generalized Pareto Distribution with parameters `m`, `lambda`, and `xi`.

SIDE EFFECTS The function `rgpd` causes the creation of `.Random.seed` if it does not already exist, otherwise its value is updated.

## Author(s)

Rene Carmona, [email protected]

## References

R. A. Carmona: Statistical Analysis of Financial Data in S-Plus, (2004) Springer Verlag

`rgev`, `gpd.lmom`, `gpd.ml`
 ``` 1 2 3 4 5 6 7 8 9 10``` ``` x <- rgev(200) # Generates a sample of size 200 from # the Gumbel distribution # Evaluation at x = 1.0 of GEV density functions # with different parameters m <- c(0,0,0) lambda <- c(1.3, 1.0, .7) xi <- c(-0.2,0.0,0.2) x <- rep(1.0,3) pgev(x,m,lambda,xi) ```