The Generalized Pareto Distribution
Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GenPareto) with location, scale and shape parameters.
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)
x, q |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
loc, scale, shape |
Location, scale and shape parameters; the
|
log |
Logical; if |
lower.tail |
Logical; if |
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.
dGenPareto gives the density function, pGenPareto gives the
distribution function, qGenPareto gives the quantile function,
and rGenPareto generates random deviates.
Alec Stephenson <alec_stephenson@hotmail.com>
Pickands, J. (1975) Statistical inference using Extreme Order statistics. Annals of Statistics, 3, 119–131.
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
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