gpd {evd} | R Documentation

## The Generalized Pareto Distribution

### Description

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

### Usage

    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 `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

`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.

### See Also

`fpot`, `rgev`

### Examples

    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)
    ## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

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