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; } Fig4: Hazard rate function of EMDL random variable for selected parameter values Mentions: From (3) and (6) it is easy to verify that the hazard rate function of X is7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\begin{aligned} h\left( x\right)&=\,\frac{f\left( x\right) }{S\left( x\right) } =\beta \frac{\left( 3-r\right) }{\left( 1-r\right) \left( 3-2r\right) }=\beta \left[ 1+2\frac{r\left( 2-r\right) }{\left( 1-r\right) \left( 3-2r\right) }\right] \\&=\,\beta \left[ \frac{2}{\left( 1-r\right) }-\frac{3}{\left( 3-2r\right) }\right] \end{aligned}\end{document}hx=fxSx=β3-r1-r3-2r=β1+2r2-r1-r3-2r=β21-r-33-2rwith and where . As it can be seen immediately from last two statements on the right side of (7), h(x) is a monotonically decreasing function and bounded from below with (see Fig. 4).Fig. 4

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

Mentions: From (3) and (6) it is easy to verify that the hazard rate function of X is7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\begin{aligned} h\left( x\right)&=\,\frac{f\left( x\right) }{S\left( x\right) } =\beta \frac{\left( 3-r\right) }{\left( 1-r\right) \left( 3-2r\right) }=\beta \left[ 1+2\frac{r\left( 2-r\right) }{\left( 1-r\right) \left( 3-2r\right) }\right] \\&=\,\beta \left[ \frac{2}{\left( 1-r\right) }-\frac{3}{\left( 3-2r\right) }\right] \end{aligned}\end{document}hx=fxSx=β3-r1-r3-2r=β1+2r2-r1-r3-2r=β21-r-33-2rwith and where . As it can be seen immediately from last two statements on the right side of (7), h(x) is a monotonically decreasing function and bounded from below with (see Fig. 4).Fig. 4