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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

Article Details

Author Biographies

Anum Fatima, Lahore College for Women University, Lahore.

Student, Statistics Department Lahore College for Women University, Lahore.

Ayesha Roohi, Lahore College for Women University, Lahore.

Dean Humanities and Social Sciences, HOD Statistics Department, Lahore College for Women University, Lahore.
How to Cite
Fatima, A., & Roohi, A. (2015). Extended Poisson Exponential Distribution. Pakistan Journal of Statistics and Operation Research, 11(3), 361-375. https://doi.org/10.18187/pjsor.v11i3.708