gpd {smoothtail} | R Documentation |
The Generalized Pareto Distribution
Description
Density function, distribution function, quantile function and
random generation for the generalized Pareto distribution (GPD) with shape parameter \gamma
and
scale parameter \sigma
.
Usage
dgpd(x, gam, sigma = 1)
pgpd(q, gam, sigma = 1)
qgpd(p, gam, sigma = 1)
rgpd(n, gam, sigma = 1)
Arguments
x , q |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
gam |
Shape parameter, real number. |
sigma |
Scale parameter, positive real number. |
Details
The generalized Pareto distribution function (Pickands, 1975) with
shape parameter \gamma
and scale parameter \sigma
is
W_{\gamma,\sigma}(x) = 1 - {(1+\gamma x / \sigma)}_+^{-1/\gamma}.
If \gamma = 0
, the distribution function is defined by continuity. The density is denoted by
w_{\gamma, \sigma}
.
Value
dgpd
gives the values of the density function, pgpd
those of the distribution
function, and qgpd
those of the quantile function of the GPD at {\bold x}, {\bold q},
and {\bold p}
,
respectively. rgpd
generates n
random numbers, returned as an ordered vector.
Author(s)
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Samuel Mueller, samuel.mueller@sydney.edu.au,
www.maths.usyd.edu.au/ut/people?who=S_Mueller
References
Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3, 119-131.
See Also
Similar functions are provided in the R-packages evir and evd.