Distribution function and quantile function
of the generalized Pareto distribution.
Usage
cdfgpa(x, para = c(0, 1, 0))
quagpa(f, para = c(0, 1, 0))
Arguments
x
Vector of quantiles.
f
Vector of probabilities.
para
Numeric vector containing the parameters of the distribution,
in the order $\xi, \alpha, k$ (location, scale, shape).
Value
cdfgpa gives the distribution function;
quagpa gives the quantile function.
Details
The generalized Pareto distribution with
location parameter $\xi$,
scale parameter $\alpha$ and
shape parameter $k$ has distribution function
$$F(x)=1-\exp(-y)$$ where
$$y=-k^{-1}\log(1-k(x-\xi)/\alpha),$$
with $x$ bounded by $\xi+\alpha/k$
from below if $k<0$ and="" from="" above="" if="" $k="">0$,
and quantile function
$$x(F)=\xi-{\alpha\over k}(1-(1-F)^k).$$
The exponential distribution is the special case $k=0$.
The uniform distribution is the special case $k=1$.
See Also
cdfexp for the exponential distribution.
cdfkap for the kappa distribution and
cdfwak for the Wakeby distribution,
which generalize the generalized Pareto distribution.