ProbEPD function

Estimator of small exceedance probabilities and large return periods using EPD

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.

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.

Returns

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.

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.

Author(s)

Tom Reynkens

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))