# ProbEPD: 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 parameters from the EPD fit.

## Usage

 ```1 2 3 4 5``` ```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.

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.

`EPD`, `Prob`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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)) ```

### Example output   ```
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ReIns documentation built on July 2, 2020, 4:03 a.m.