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)
data |
Vector of n observations. |
tau |
Value for the τ 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 γ and the second element is the starting value for the estimator of κ. Default is |
warnings |
Logical indicating if possible warnings from the optimisation function are shown, default is |
See Section 4.2.1 of Albrecher et al. (2017) for more details.
A vector with the MLE estimate for the γ parameter of the EPD as the first component and the MLE estimate for the κ parameter of the EPD as the second component.
Tom Reynkens
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 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)
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