Exponential-modified discrete Lindley distribution View Article: PubMed Central - PubMed ABSTRACTIn this study, we have considered a series system composed of stochastically independent M-component where M is a random variable having the zero truncated modified discrete Lindley distribution. This distribution is newly introduced by transforming on original parameter. The properties of the distribution of the lifetime of above system have been examined under the given circumstances and also parameters of this new lifetime distribution are estimated by using moments, maximum likelihood and EM-algorithm. No MeSH data available. © Copyright Policy - OpenAccess Related In: Results  -  Collection License getmorefigures.php?uid=PMC5037113&req=5 .flowplayer { width: px; height: px; } Fig1: P.m.f of geometric, negative binomial and modified discrete Lindley Mentions: If p.m.f in (2) is rewritten as the following form\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P\left( M=m\right) =\frac{\theta }{1+\theta }\left[ \theta {\left( 1-\theta \right) }^m\right] +\frac{1}{1+\theta }\left[ {\theta }^2\left( m+1\right) {\left( 1-\theta \right) }^m\right] =w_1f_1\left( m\right) +w_2f_2\left( m\right),$$\end{document}PM=m=θ1+θθ1-θm+11+θθ2m+11-θm=w1f1m+w2f2m,then indicates p.m.f of a geometric random variable with success probability and indicates p.m.f of a negative binomial random variable which denotes the number of trials until the second success, with common success probability . and denote component probabilities; in other words these are called the mixture weights (Fig. 1).

Exponential-modified discrete Lindley distribution
Related In: Results  -  Collection

Mentions: If p.m.f in (2) is rewritten as the following form\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P\left( M=m\right) =\frac{\theta }{1+\theta }\left[ \theta {\left( 1-\theta \right) }^m\right] +\frac{1}{1+\theta }\left[ {\theta }^2\left( m+1\right) {\left( 1-\theta \right) }^m\right] =w_1f_1\left( m\right) +w_2f_2\left( m\right),$$\end{document}PM=m=θ1+θθ1-θm+11+θθ2m+11-θm=w1f1m+w2f2m,then indicates p.m.f of a geometric random variable with success probability and indicates p.m.f of a negative binomial random variable which denotes the number of trials until the second success, with common success probability . and denote component probabilities; in other words these are called the mixture weights (Fig. 1).