Some Statistical Properties of Mixture Distribution and Its Applications to Monte Carlo Simulation and Particle Filter

概要

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This paper aims to study some statistical properties of mixture distribution, especiallay on its mean, variance, skewness, and kurtosis. From these properties, we find a mixture distribution can provide an accurate approximate for a probability distribution function for observed data, even for a distribution with heavy tails, excess kurtosis, and finite moments. Sometimes, it is important since these phenomena are well observed in financial markets and some scientific fields. Here, in this paper, we also propose an algorithm to generate random numbers from mixture distribution, and it can be utilized in dealing with Monte Carlo simulation and particle filter under the circumstances of mixture distributions. Furthermore, we propose some algorithms to estimate the structure of particle filter and its parameters based upon Genetic Programming and Genetic Algorithm.
久留米大学の論文