ldwm: Log-likelihood of dynamically weighted mixture model

Description

Log-likelihood and negative log-likelihood for the dynamically weighted mixture model

Usage

ldwm(x, wshape = 1, wscale = 1, cmu = 1, ctau = 1,
    sigmau = sqrt(wscale^2 * gamma(1 + 2/wshape) - (wscale * gamma(1 + 1/wshape))^2),
    xi = 0, log = TRUE)

  nldwm(pvector, x, finitelik = FALSE)

Arguments

vector of sample data

pvector

vector of initial values of mixture model parameters (wshape, wscale, cmu, ctau, sigmau, xi) or NULL

finitelik

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

wshape

Weibull shape (non-negative)

wscale

Weibull scale (non-negative)

cmu

Cauchy location

ctau

Cauchy scale

sigmau

scale parameter (non-negative)

shape parameter

log

logical, if TRUE then log density

Value

ldwm gives (log-)likelihood and nldwm gives the negative log-likelihood.

Details

The likelihood functions for the dynamically weighted mixture model fdwm. Non-positive data are ignored. They are designed to be used for MLE in fdwm but are available for wider usage, e.g. constructing your own extreme value mixture models. See fdwm and fgpd for full details. Log-likelihood calculations are carried out in ldwm, which takes parameters as inputs in the same form as distribution functions. The negative log-likelihood is a wrapper for ldwm, designed towards making it useable for optimisation (e.g. parameters are given a vector as first input). The function ldwm 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/Weibull_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 Frigessi, A., O. Haug, and H. Rue (2002). A dynamic mixture model for unsupervised tail estimation without threshold selection. Extremes 5 (3), 219-235