A global optimisation approach for parameter estimation of a mixture of double Pareto lognormal and lognormal distributions

Abstract

The double Pareto Lognormal(dPlN) statistical distribution, defined interms of both an exponentiated skewed Laplace distribution and alog normal distribution, has proven suitable for fitting heavy tailed data. In this work we investigate inference for the mixture of a dPlN component and ðk 1Þ lognormal components for k fixed,amodelforextremeandskeweddatawhichadditionallycapturesmulti- modality. The optimisationcriterionbasedonthelikelihoodmaximisationisconsidered,whichyieldsaglobal optimisation problem with an objective function difficult to evaluate and optimise. Variable Neighbour- hood Search(VNS)is proven to be a powerful tool to over come such difficulties. Our approach is illustrated with both simulated and real data, in which our VNS and a standard multistart are compared. The computationalexperienceshowsthattheVNSismorestablenumericallyandprovidesslightly better objective values.