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