ProbMOM: Estimator of small exceedance probabilities and large return... In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Description

Computes estimates of a small exceedance probability P(X>q) or large return period 1/P(X>q) using the Method of Moments estimates for the EVI.

Usage

 1 2 3 4 5 ProbMOM(data, gamma, q, plot = FALSE, add = FALSE, main = "Estimates of small exceedance probability", ...) ReturnMOM(data, gamma, q, plot = FALSE, add = FALSE, main = "Estimates of large return period", ...)

Arguments

 data Vector of n observations. gamma Vector of n-1 estimates for the EVI obtained from Moment. q The used large quantile (we estimate P(X>q) or 1/P(X>q) for q large). plot Logical indicating if the estimates should be plotted as a function of k, default is FALSE. add Logical indicating if the estimates should be added to an existing plot, default is FALSE. main Title for the plot, default is "Estimates of small exceedance probability" for ProbMOM and "Estimates of large return period" for ReturnMOM. ... Additional arguments for the plot function, see plot for more details.

Details

See Section 4.2.2 of Albrecher et al. (2017) for more details.

Value

A list with following components:

 k Vector of the values of the tail parameter k. P Vector of the corresponding probability estimates, only returned for ProbMOM. R Vector of the corresponding estimates for the return period, only returned for ReturnMOM. q The used large quantile.

Tom Reynkens.

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

Beirlant J., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.

Dekkers, A.L.M, Einmahl, J.H.J. and de Haan, L. (1989). "A Moment Estimator for the Index of an Extreme-value Distribution." Annals of Statistics, 17, 1833–1855.  