Separation and Lack of Separation of Subpopulation in the Mixed Distributions

Abstract

This is a comparative study between the estimates of parameters of mixed distributions in the case of the possibility of separating the units of subpopulation or the absence of that possibility under the progressive type I censored test data. An iterative procedure is developed and tested numerically to obtain new estimators and their variance–covariance matrix. Finally, we will use the exact distribution of the maximum likelihood estimators as well as its asymptotic distribution and the parametric bootstrap method; then, we will discuss the construction of confidence intervals for the mean parameter and their performance is assessed through Monte Carlo simulations.

Keywords:

• Asymptotic variance–covariance matrix
• Bootstrap method
• Finite mixture
• Maximum likelihood estimation
• Rayleigh distribution
• Type I progressive censored

Acknowledgments

The author would like to thank the editor and the referees for their helpful comments, which improved the presentation of the article.