Generalized Pareto {POT} | R Documentation |
Density, distribution function, quantile function and random generation for the GP distribution with location equal to 'loc', scale equal to 'scale' and shape equal to 'shape'.
rgpd(n, loc = 0, scale = 1, shape = 0) pgpd(q, loc = 0, scale = 1, shape = 0, lower.tail = TRUE) qgpd(p, loc = 0, scale = 1, shape = 0, lower.tail = TRUE) dgpd(x, loc = 0, scale = 1, shape = 0, log = FALSE)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. |
loc |
vector of the location parameters. |
scale |
vector of the scale parameters. |
shape |
a numeric of the shape parameter. |
lower.tail |
logical; if TRUE (default), probabilities are P[ X <= x], otherwise, P[X > x]. |
log |
logical; if TRUE, probabilities p are given as log(p). |
If 'loc', 'scale' and 'shape' are not specified they assume the default
values of '0', '1' and '0', respectively.
The GP distribution function for loc = μ, scale = σ
and shape = xi is
G(z) = 1 - [ 1 + xi ( z - μ ) / σ ]^(-1/xi)
for 1 + xi ( z - μ ) / σ > 0 and z > μ, where
σ > 0. If
xi = 0, the distribution is defined by continuity corresponding to
the exponential distribution.
dgpd(0.1) rgpd(100, 1, 2, 0.2) qgpd(seq(0.1, 0.9, 0.1), 1, 0.5, -0.2) pgpd(12.6, 2, 0.5, 0.1)