American Journal of Modeling and Optimization
ISSN (Print): 2333-1143 ISSN (Online): 2333-1267 Website: http://www.sciepub.com/journal/ajmo Editor-in-chief: Dr Anil Kumar Gupta
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American Journal of Modeling and Optimization. 2016, 4(1), 19-28
DOI: 10.12691/ajmo-4-1-3
Open AccessArticle

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

Salah H Abid1, and Sajad H Mohammed1

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

Pub. Date: May 03, 2016

Cite this paper:
Salah H Abid and 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

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.

Keywords:
Weibull-Poisson distribution inverse Weibull-Poisson distribution Shannon entropy Rényi entropy Relative entropy stress-strength reliability

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References:

[1]  Abramowitz, M. and Stegun, I. (1970). “Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables”, 9-Revised edition, Dover Publications, USA.
 
[2]  Bera, W. (2015). “The Kumaraswamy inverse Weibull Poisson distributions with applications”, MSc thesis of mathematics, Indiana University of Pennsylvania.
 
[3]  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.
 
[4]  Hassan, A., Abd-Elfattah, A. and Moktar, A. (2016). “The Complementary Exponentiated Inverted Weibull Power Series Family of Distributions and its Applications”, British Journal of Mathematics & Computer Science 13(2): 1-20.
 
[5]  Percontini, A., Blas, B. and Cordeiro, G. (2013). “The Beta Weibull Poisson distribution”, Chilean Journal of statistics, Vol.4, No.2, P.3-26.