Generalized Pareto distribution
Distribution function and quantile function of the generalized Pareto distribution.
cdfgpa(x, para = c(0, 1, 0)) quagpa(f, para = c(0, 1, 0))
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). |
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 = (-1/k) 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 (1 - (1-F)^k) / k .
The exponential distribution is the special case k=0. The uniform distribution is the special case k=1.
cdfgpa gives the distribution function;
quagpa gives the quantile function.
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
distribution functions pnorm, qnorm, etc.
cdfexp for the exponential distribution.
# Random sample from the generalized Pareto distribution # with parameters xi=0, alpha=1, k=-0.5. quagpa(runif(100), c(0,1,-0.5))
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.