Finite mixtures of MaxEnt distributions

Abstract

Mixture distribution analysis has been the subject of a large remarkable diverse body of literature. So, in order to obtain a mixture density, the problem of parameter estimation has arisen and has taken an important role in this analysis. Parameter estimation is required not only for the parameters of the mixture component but also for the mixture proportion. Widely used method for this problem has been maximum likelihood whereas there are a number of specialized procedures such as least-squares criterion, graphical procedure, etc. In this study, in order to model mixture density, mixture of MaxEnt distributions is proposed instead of mixture of familiar distributions. Since MaxEnt distributions are non-parametric distributions, the problem is reduced to parameter estimation only for mixture proportion. Then, maximum equality estimator which also is based on Shannon’s entropy measure is proposed to be used. It is proved that the mixture of MaxEnt distributions is identifiable and gives more accurate fitting values rather than the mixture of familiar distributions without constructing the likelihood function.