gpd

0th

Percentile

The Generalized Pareto Distribution

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

Keywords
distribution
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 $\code{loc} = a$, $\code{scale} = b$ 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.

See Also

fpot, rgev

Aliases
  • dgpd
  • pgpd
  • qgpd
  • rgpd
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
Documentation reproduced from package evd, version 2.1-0, License: GPL (Version 2 or above)

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