Optimal Subsampling of Finite Mixture Distribution

Abstract

<p> A mixture distribution is a compounding of statistical distributions, which arises when sampling from heterogeneous populations with a different probability density function in each component. A finite mixture has a finite number of components. In the past decade the extent and the potential of the applications of finite mixture models have widened considerably.</p> <p> The objective of this project is to add some functionalities to a package 'mixdist' developed by Du and Macdonald (Du 2002) and Gao (2004) in the R environment (R Development Core Team 2004) for estimating the parameters of a finite mixture distribution with data grouped in bins and conditional data. Mixed data together with conditional data will provide better estimates of parameters than do mixed data alone. Our main objective is to obtain the optimal sample size for each bin of the mixed data to obtain conditional data, given approximate values of parameters and the distributional form of the mixture for the given data. We have also replaced the dependence of the function mix upon the optimizer nlm to optimizer optim to provide the limits to the parameters.</p> <p> Our purpose is to provide easily available tools to modeling fish growth using mixture distribution. However, it has a number of applications in other areas as well.</p>