egp: Extended generalised Pareto families

In lbelzile/mev: Modelling of Extreme Values

Extended generalised Pareto families

Description

This function provides the log-likelihood and quantiles for the three different families presented in Papastathopoulos and Tawn (2013) and the two proposals of Gamet and Jalbert (2022), plus exponential tilting. All of the models contain an additional parameter, \kappa \ge 0. All families share the same tail index as the generalized Pareto distribution, while allowing for lower thresholds. For most models, the distribution reduce to the generalised Pareto when \kappa=1 (for models gj-tnorm and logist, on the boundary of the parameter space when kappa \to 0.

egp.retlev gives the return levels for the extended generalised Pareto distributions

Arguments

xdat	vector of observations, greater than the threshold
thresh	threshold value
par	parameter vector (\kappa, \sigma, \xi).
model	a string indicating which extended family to fit
show	logical; if TRUE, print the results of the optimization
p	extreme event probability; p must be greater than the rate of exceedance for the calculation to make sense. See Details.
plot	logical; if TRUE, a plot of the return levels

Details

For return levels, the p argument can be related to T year exceedances as follows: if there are n_y observations per year, than take p to equal 1/(Tn_y) to obtain the T-years return level.

Value

egp.ll returns the log-likelihood value.

egp.retlev returns a plot of the return levels if plot=TRUE and a matrix of return levels.

Usage

egp.ll(xdat, thresh, model, par)

egp.retlev(xdat, thresh, par, model, p, plot=TRUE)

Author(s)

Leo Belzile

References

Papastathopoulos, I. and J. Tawn (2013). Extended generalised Pareto models for tail estimation, Journal of Statistical Planning and Inference 143(3), 131–143, <doi:10.1016/j.jspi.2012.07.001>.

Gamet, P. and Jalbert, J. (2022). A flexible extended generalized Pareto distribution for tail estimation. Environmetrics, 33(6), <doi:10.1002/env.2744>.

Examples

set.seed(123)
xdat <- mev::rgp(1000, loc = 0, scale = 2, shape = 0.5)
par <- fit.egp(xdat, thresh = 0, model = 'gj-beta')$par
p <- c(1/1000, 1/1500, 1/2000)
# With multiple thresholds
th <- c(0, 0.1, 0.2, 1)
opt <- tstab.egp(xdat, th, model = 'gj-beta')
egp.retlev(xdat, opt$thresh, opt$par, 'gj-beta', p = p)
opt <- tstab.egp(xdat, th, model = 'pt-power', plots = NA)
egp.retlev(xdat, opt$thresh, opt$par, 'pt-power', p = p)

lbelzile/mev documentation built on June 14, 2025, 6:40 p.m.