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.
Highlights
Mixture of distributions is arising naturally and discussed where a statistical population has more than two sub populations
In the biology the direct applications of the mixture models are discussed by Bhattacharya [1] and by Gregor [2], in the medicine are presented by Chivers [3] and by Burekhardt [4], in the social sciences are observed by Harris [5], in an economics are mentioned by Jedidi et al [6], in the reliability and survival are analyzed by Sultan et al [7], in the life testing are suggested by Shawky and Bakoban [8], in the industrial engineering are observed by Ali et al [9]
It is revealed that the distribution of the 3-component mixture of Rayleigh distributions is positively skewed because the value of mean is greater than median and SK > 0
Summary
Mixture of distributions is arising naturally and discussed where a statistical population has more than two sub populations. Several authors have worked on the mixture modeling. This study plan to develop a 3-component mixture of Rayleigh distributions for an effective modeling of time-to-failure data. A variable of interest y which follows a mixture distribution having q components and its density function is f y = wm fm y , where m=1 wm The pdf and cdf m=1 of 3-component mixture of Rayleigh distributions for the unknown mixing proportions w1 and w2 is defined as follows:.
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