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.

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)
##  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9


[Package DescTools version 0.99.51 Index]