ReIns (version 1.0.10)

ProbEPD: 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", ...)

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.

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.

Author

Tom Reynkens

Details

See Section 4.2.1 of Albrecher et al. (2017) for more details.

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))