EPDfit function

Fit EPD using MLE

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

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.

Details

See Section 4.2.1 of Albrecher et al. (2017) for more details.

Returns

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.

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, GPDfit

Examples

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)