evd (version 2.1-0)

gpd: 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]

Value

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

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.

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