ProbEPD: Estimator of small exceedance probabilities and large return...

In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Estimator of small exceedance probabilities and large return periods using EPD

Description

Computes estimates of a small exceedance probability P(X>q) or large return period 1/P(X>q) using the parameters from the EPD fit.

Usage

ProbEPD(data, q, gamma, kappa, tau, plot = FALSE, add = FALSE, 
        main = "Estimates of small exceedance probability", ...)

ReturnEPD(data, q, gamma, kappa, tau, plot = FALSE, add = FALSE, 
          main = "Estimates of large return period", ...)

Arguments

data	Vector of n observations.
q	The used large quantile (we estimate P(X>q) or 1/P(X>q) for q large).
gamma	Vector of n-1 estimates for the EVI obtained from EPD.
kappa	Vector of n-1 estimates for \kappa obtained from EPD.
tau	Vector of n-1 estimates for \tau obtained from EPD.
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 ProbEPD and "Estimates of large return period" for ReturnEPD.
...	Additional arguments for the plot function, see plot for more details.

Details

See Section 4.2.1 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 ProbEPD.
R	Vector of the corresponding estimates for the return period, only returned for ReturnEPD.
q	The used large quantile.

Author(s)

Tom Reynkens

References

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

Beirlant, J., Joossens, E. and Segers, J. (2009). "Second-Order Refined Peaks-Over-Threshold Modelling for Heavy-Tailed Distributions." Journal of Statistical Planning and Inference, 139, 2800–2815.

See Also

EPD, Prob

Examples

data(secura)

# EPD estimates for the EVI
epd <- EPD(secura$size, plot=TRUE)

# Compute exceedance probabilities
q <- 10^7
ProbEPD(secura$size, q=q, gamma=epd$gamma, kappa=epd$kappa, tau=epd$tau, plot=TRUE)

# Compute return periods
ReturnEPD(secura$size, q=q, gamma=epd$gamma, kappa=epd$kappa, tau=epd$tau, 
          plot=TRUE, ylim=c(0,10^4))

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.