Abstract
This paper presents Rayleigh mixtures of distributions in which the weight functions are assumed to be chi‐square, t and F sampling distributions. The exact probability density functions of the mixture of two correlated Rayleigh random variables have been derived. Different moments, characteristic functions, shape characteristics, and the estimates of the parameters of the proposed mixture distributions using method of moments have also been provided.
Highlights
In statistics, a mixture distribution is expressed as a convex combination of other probability distributions
In this paper we first define the general form of Rayleigh mixture distribution
We have presented the Rayleigh mixtures of distributions in which the weight functions are assumed to be chi-square, t- and F-distributions, and the mixture of two correlated Rayleigh distributions has been presented
Summary
A mixture distribution is expressed as a convex combination of other probability distributions. Mixture distribution may suitably be used for certain data set where different subsets of the whole data set possess different properties that can best be modeled separately. They can be more mathematically manageable, because the individual mixture components are dealt with more nicely than the overall mixture density. Pearson 1 is considered as the torch bearer in the field of mixtures distributions. He studied the estimation of the parameters of the mixture of two normal distributions. In the light of the above-mentioned distributions, here we have studied Rayleigh mixtures of Journal of Applied Mathematics distributions in which the weight functions are assumed to be chi-square, t- and F-distribution, and the moments, characteristic function, and shape characteristics of these mixtures distributions have been studied
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