GPDfit function

Fit GPD using MLE

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

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.

Returns

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.

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.

Author(s)

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

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])