R arm of morie.fn.gpdD and gpfit. GpdDistribution:
CDF, density, quantiles, mean and variance of the GPD
\(F(x) = 1 - (1 + \xi x/\sigma)^{-1/\xi}\). Gpfit: peaks over
threshold, the maximum likelihood fit of the excesses over threshold
(default the type-7 90th percentile), started from
morie_evt_gpd_mle and refined by Newton steps on the analytic score and Hessian;
standard errors from the observed information.
Usage
GpdDistribution(sigma, xi, x = c(0.5, 1, 2, 4), p = c(0.5, 0.9, 0.95, 0.99))
Gpfit(x, threshold = NULL)
Arguments
- sigma
Scale, positive.
- xi
Shape.
- x
Points (GpdDistribution) or raw observations (Gpfit).
- p
Probabilities.
- threshold
Threshold.
Value
A list (the Python payload).
References
Pickands, J. (1975). Statistical inference using extreme order
statistics. Annals of Statistics 3, 119-131.
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme
Values. Springer.
Examples
GpdDistribution(2, 0.25, x = c(1, 3), p = c(0.5, 0.9))$cdf
#> [1] 0.3757049 0.7202377
Gpfit(c(0.2, 1.4, 0.7, 2.9, 0.3, 5.1, 1.1, 0.9, 3.8, 0.5, 2.2, 7.4, 1.8, 0.6, 4.3), 0.5)$shape
#> [1] -0.1801363
