lhpd: Log-likelihood of Hybrid Pareto Extreme Value Mixture Model

Description

Log-likelihood and negative log-likelihood for the hybrid Pareto extreme value mixture model

Usage

lhpd(x, nmean = 0, nsd = 1, xi = 0, log = TRUE)

  nlhpd(pvector, x, finitelik = FALSE)

Arguments

vector of sample data

nmean

normal mean

nsd

normal standard deviation (non-negative)

shape parameter

log

logical, if TRUE then log density

pvector

vector of initial values of mixture model parameters (nmean, nsd, u, sigmau, xi) or NULL

finitelik

logical, should log-likelihood return finite value for invalid parameters

Value

lhpd gives (log-)likelihood and nlhpd gives the negative log-likelihood.

Details

The likelihood functions for hybrid Pareto extreme value mixture model, as used in the maximum likelihood fitting function fhpd. They are designed to be used for MLE in fhpd but are available for wider usage, e.g. constructing your own extreme value mixture models. See fhpd and fgpd for full details. Log-likelihood calculations are carried out in lhpd, which takes parameters as inputs in the same form as distribution functions. The negative log-likelihood is a wrapper for lhpd, designed towards making it useable for optimisation (e.g. parameters are given a vector as first input). The function lhpd carries out the calculations for the log-likelihood directly, which can be exponentiated to give actual likelihood using (log=FALSE).

References

http://en.wikipedia.org/wiki/Normal_distribution http://en.wikipedia.org/wiki/Generalized_Pareto_distribution Scarrott, C.J. and MacDonald, A. (2012). A review of extreme value threshold estimation and uncertainty quantification. REVSTAT - Statistical Journal 10(1), 33-59. Available from http://www.ine.pt/revstat/pdf/rs120102.pdf Carreau, J. and Y. Bengio (2008). A hybrid Pareto model for asymmetric fat-tailed data: the univariate case. Extremes 12 (1), 53-76.