On Finite 3-Component Mixture of Rayleigh Distributions: A Classical Look

Abstract

In this study, we have discussed various statistical properties for 3-component mixture of Rayleigh distributions. Here initially, the main properties of mixture distributions are presented and analyzed. Second, some of the famous entropies, measures of inequality are also discussed. Also, the statistical properties of the density functions of rth-, 1st- and nth-order statistics are derived. Moreover, the parameters estimation of the considered mixture model under the maximum likelihood (ML) estimation is also performed using censored and complete data scheme. Finally, the results on ML estimation are also computed via Monte Carlo simulation study and as well as by using a real-life data set.

Keywords

• Mixture distribution
• Maximum likelihood estimation
• Statistical properties
• Entropies
• Inequality measures
• Order statistics