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
$$y=-k^{-1}\log\lbrace1-k(x-\xi)/\alpha\rbrace,$$
with \(x\) bounded by \(\xi+\alpha/k\)
from below if \(k<0\) and from above if \(k>0\),
and quantile function
$$x(F)=\xi+{\alpha\over k}\lbrace 1-(1-F)^k\rbrace.$$
The exponential distribution is the special case \(k=0\).
The uniform distribution is the special case \(k=1\).