ReIns (version 1.0.7)

EPDfit: Fit EPD using MLE

Description

Fit the Extended Pareto Distribution (EPD) to data using Maximum Likelihood Estimation (MLE).

Usage

EPDfit(data, tau, start = c(0.1, 1), warnings = FALSE)

Arguments

data

Vector of \(n\) observations.

tau

Value for the \(\tau\) parameter of the EPD.

start

Vector of length 2 containing the starting values for the optimisation. The first element is the starting value for the estimator of \(\gamma\) and the second element is the starting value for the estimator of \(\kappa\). Default is c(0.1,1).

warnings

Logical indicating if possible warnings from the optimisation function are shown, default is FALSE.

Value

A vector with the MLE estimate for the \(\gamma\) parameter of the EPD as the first component and the MLE estimate for the \(\kappa\) parameter of the EPD as the second component.

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, GPDfit

Examples

# NOT RUN {
data(soa)

# Look at last 500 observations of SOA data
SOAdata <- sort(soa$size)[length(soa$size)-(0:499)]

# Fit EPD to last 500 observations
res <- EPDfit(SOAdata/sort(soa$size)[500], tau=-1)
# }