ReIns: ProbEPD – R documentation

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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", ...)

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 κ obtained from `EPD`.
`tau`	Vector of n-1 estimates for τ 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.

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

Functions from "Reinsurance: Actuarial and Statistical Aspects"

v1.0.10

GPL (>= 2)

Authors

Tom Reynkens [aut, cre] (<https://orcid.org/0000-0002-5516-5107>), Roel Verbelen [aut] (R code for Mixed Erlang distribution, <https://orcid.org/0000-0002-2347-9240>), Anastasios Bardoutsos [ctb] (Original R code for cEPD estimator), Dries Cornilly [ctb] (Original R code for EVT estimators for truncated data), Yuri Goegebeur [ctb] (Original S-Plus code for basic EVT estimators), Klaus Herrmann [ctb] (Original R code for GPD estimator)

Initial release

2020-05-16