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.
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.
Author
Tom Reynkens
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.
data(soa)
# Look at last 500 observations of SOA dataSOAdata <- sort(soa$size)[length(soa$size)-(0:499)]
# Fit EPD to last 500 observationsres <- EPDfit(SOAdata/sort(soa$size)[500], tau=-1)