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Exponential-modified discrete Lindley distribution

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ABSTRACT

In 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.


P.m.f of geometric, negative binomial and modified discrete Lindley
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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
P.m.f of geometric, negative binomial and modified discrete Lindley
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037113&req=5

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).

View Article: PubMed Central - PubMed

ABSTRACT

In 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.