gpd {evd} | R Documentation |
Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GPD) with location, scale and shape parameters.
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)
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] |
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.
dgpd
gives the density function, pgpd
gives the
distribution function, qgpd
gives the quantile function,
and rgpd
generates random deviates.
Pickands, J. (1975) Statistical inference using extreme order statistics. Annals of Statistics, 3, 119–131.
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