GPDfit {ReIns}

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)

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.

Details

See Section 4.2.2 in Albrecher et al. (2017) for more details.

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.

Author(s)

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

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])