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DeMorais, A. (2009). “A class of generalized Beta distributions, Pareto power series and Weibull power series”, MSc thesis of statistics, Federal University of De Pernambuco.

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Article

Properties of the Distributions Generated by Mixing Weibull and Inverse Weibull Distributions with Zero Truncated Poisson

1Mathematics department, Education College, Al-Mustansiriya University, Baghdad, Iraq


American Journal of Modeling and Optimization. 2016, Vol. 4 No. 1, 19-28
DOI: 10.12691/ajmo-4-1-3
Copyright © 2016 Science and Education Publishing

Cite this paper:
Salah H Abid, Sajad H Mohammed. Properties of the Distributions Generated by Mixing Weibull and Inverse Weibull Distributions with Zero Truncated Poisson. American Journal of Modeling and Optimization. 2016; 4(1):19-28. doi: 10.12691/ajmo-4-1-3.

Correspondence to: Salah  H Abid, Mathematics department, Education College, Al-Mustansiriya University, Baghdad, Iraq. Email: abidsalah@gmail.com

Abstract

In reliability analysis, a lot of failure distributions are used to represent lifetime data. Recently, new distributions are derived to extend some of well-known families of distributions, such that the new distributions are more flexible than the others to model real data. In this paper, properties of Weibull-Poisson distribution (WPD) and inverse Weibull-Poisson distribution (IWPD) will be considered. We provide forms for characteristic function, rth raw moment, mean, variance, median, Shannon entropy function, Rényi entropy function and Relative entropy function. This paper deals also with the determination of R = P[Y < X] when X and Y are two independent WPD (IWPD) distributions with different parameters.

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