Extended Poisson Exponential Distribution

Anum Fatima, Ayesha Roohi

Abstract


A new mixture of Modified Exponential (ME) and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.


Keywords


Modified Exponential distribution, Information entropies, Maximum Likelihood Estimates, Moments, Order Statistics

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DOI: http://dx.doi.org/10.18187/pjsor.v11i3.708

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Copyright (c) 2015 Pakistan Journal of Statistics and Operation Research

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Title

Extended Poisson Exponential Distribution

Keywords

Modified Exponential distribution, Information entropies, Maximum Likelihood Estimates, Moments, Order Statistics

Description

A new mixture of Modified Exponential (ME) and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.


Date

2015-09-08

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 11 No. 3, 2015



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810