# gpd: The Generalized Pareto Distribution In evd: Functions for Extreme Value Distributions

## Description

Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GPD) with location, scale and shape parameters.

## Usage

 ```1 2 3 4``` ```dgpd(x, loc=0, scale=1, shape=0, log = FALSE) pgpd(q, loc=0, scale=1, shape=0, lower.tail = TRUE) qgpd(p, loc=0, scale=1, shape=0, lower.tail = TRUE) rgpd(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 generalized Pareto distribution function (Pickands, 1975) with parameters \code{loc} = a, \code{scale} = b and \code{shape} = s is

G(z) = 1 - {1+s(z-a)/b}^(-1/s)

for 1+s(z-a)/b > 0 and z > a, where b > 0. If s = 0 the distribution is defined by continuity.

## Value

`dgpd` gives the density function, `pgpd` gives the distribution function, `qgpd` gives the quantile function, and `rgpd` generates random deviates.

## References

Pickands, J. (1975) Statistical inference using extreme order statistics. Annals of Statistics, 3, 119–131.

`fpot`, `rgev`

## Examples

 ```1 2 3 4 5 6 7``` ```dgpd(2:4, 1, 0.5, 0.8) pgpd(2:4, 1, 0.5, 0.8) qgpd(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8) rgpd(6, 1, 0.5, 0.8) p <- (1:9)/10 pgpd(qgpd(p, 1, 2, 0.8), 1, 2, 0.8) ##  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ```

### Example output

``` 0.23299144 0.07919889 0.03831043
 0.6971111 0.8336823 0.8888998
 5.318483 3.639936 3.012506 2.675864
  1.114968  1.152077  1.052988  2.391035  3.698861 13.949017
 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
```

evd documentation built on May 1, 2019, 10:11 p.m.