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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.

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Confidence region for
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Fig7: Confidence region for

Mentions: Firstly, we present the asymptotic distribution of the ML estimates,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \sqrt{50}\left( \left[ \begin{array}{ cc} \hat{\theta } \\ \hat{\beta } \end{array}\right] -\left[ \begin{array}{ cc} 0.6 \\ 0.3 \end{array}\right] \right) \sim AN\left( \left[ \begin{array}{ cc} 0 \\ 0 \end{array}\right] ,{\left[ \begin{array}{ cc} 1.7622 & \quad -3.4018 \\ -3.4018 & \quad 10.3494 \end{array}\right] }^{-1}\right) \end{aligned}$$\end{document}50θ^β^-0.60.3∼AN00,1.7622-3.4018-3.401810.3494-1Now, let indicate the center of ellipsoid, and observed information matrix is calculated as (note that ). Then the confidence ellipsoid at the level 95 % is defined by where 5.99 is a critical value of the chi-squared distribution with two degrees of freedom with upper percentiles 95 % (Fig. 7).Fig. 7


Exponential-modified discrete Lindley distribution
Confidence region for
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5037113&req=5

Fig7: Confidence region for
Mentions: Firstly, we present the asymptotic distribution of the ML estimates,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \sqrt{50}\left( \left[ \begin{array}{ cc} \hat{\theta } \\ \hat{\beta } \end{array}\right] -\left[ \begin{array}{ cc} 0.6 \\ 0.3 \end{array}\right] \right) \sim AN\left( \left[ \begin{array}{ cc} 0 \\ 0 \end{array}\right] ,{\left[ \begin{array}{ cc} 1.7622 & \quad -3.4018 \\ -3.4018 & \quad 10.3494 \end{array}\right] }^{-1}\right) \end{aligned}$$\end{document}50θ^β^-0.60.3∼AN00,1.7622-3.4018-3.401810.3494-1Now, let indicate the center of ellipsoid, and observed information matrix is calculated as (note that ). Then the confidence ellipsoid at the level 95 % is defined by where 5.99 is a critical value of the chi-squared distribution with two degrees of freedom with upper percentiles 95 % (Fig. 7).Fig. 7

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.