A differential evolution algorithm with adaptive controlling weighted parameter for finite mixture model of some fire insurance data in Thailand

Abstract

We propose an adaptive differential evolution algorithm to estimate the parameter of finite mixture
model. The finite mixture model separates two parts of parameter set. The first part consists of a parameter set
of distributions that used for our experiment. The second part consists of a weighted parameter set of each
component that are positive real value and the combination of them equal to 1. We perform an experiment to
obtain an adaptive differential evolution algorithm for the finite mixture model by controlling the parameter set
of the second part using a technique of weighting with constant such that parameter set of the second part
satisfies condition of the finite mixture model. In this paper, we use an adaptive differential evolution algorithm
to estimate the parameter of combination of nine distributions: Rayleigh distribution, logistic distribution, gamma
distribution, Pareto distribution, log-logistic distribution, normal distribution, Weibull distribution, log-normal
distribution, and exponential distribution for 47 claimed size data of fire insurance of an insurance company in
Thailand which use K-S test statistic for the objective function. The results show that the best K-S test statistic
value of finite mixture model which equal to 0.0535 less than the best single model which equal 0.0811.
Therefore, the parameter set of the finite mixture model is 34.03 percent better.