ReIns (version 1.0.10)

GPDfit: Fit GPD using MLE

Description

Fit the Generalised Pareto Distribution (GPD) to data using Maximum Likelihood Estimation (MLE).

Usage

GPDfit(data, start = c(0.1, 1), warnings = FALSE)

Value

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

Arguments

data

Vector of \(n\) observations.

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 \(\sigma\). Default is c(0.1,1).

warnings

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

Author

Tom Reynkens based on S-Plus code from Yuri Goegebeur and R code from Klaus Herrmann.

Details

See Section 4.2.2 in 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., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.

See Also

GPDmle, EPDfit

Examples

data(soa)

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

# Fit GPD to last 500 observations
res <- GPDfit(SOAdata-sort(soa$size)[500])