R: The Generalized Pareto Distribution

GenPareto {DescTools} | R Documentation

## The Generalized Pareto Distribution

### Description

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

### Usage

    dGenPareto(x, loc=0, scale=1, shape=0, log = FALSE)
    pGenPareto(q, loc=0, scale=1, shape=0, lower.tail = TRUE)
    qGenPareto(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
    rGenPareto(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 loc = a, scale = b and 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

`dGenPareto` gives the density function, `pGenPareto` gives the distribution function, `qGenPareto` gives the quantile function, and `rGenPareto` generates random deviates.

### Author(s)

Alec Stephenson <alec_stephenson@hotmail.com>

### References

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

### See Also

`rGenExtrVal`

### Examples

    dGenPareto(2:4, 1, 0.5, 0.8)
    pGenPareto(2:4, 1, 0.5, 0.8)
    qGenPareto(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
    rGenPareto(6, 1, 0.5, 0.8)
    p <- (1:9)/10
    pGenPareto(qGenPareto(p, 1, 2, 0.8), 1, 2, 0.8)
    ## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

[Package DescTools version 0.99.32 Index]