eng
Science and Education Publishing
American Journal of Modeling and Optimization
2333-1267
2016-05-03
4
1
19
28
10.12691/ajmo-4-1-3
AJMO2016413
article
Properties of the Distributions Generated by Mixing Weibull and Inverse Weibull Distributions with Zero Truncated Poisson
Salah H Abid
abidsalah@gmail.com
1
Sajad H Mohammed
1
Mathematics department, Education College, Al-Mustansiriya University, Baghdad, Iraq
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.
http://pubs.sciepub.com/ajmo/4/1/3/ajmo-4-1-3.pdf
Weibull-Poisson distribution
inverse Weibull-Poisson distribution
Shannon entropy
Rényi entropy
Relative entropy
stress-strength reliability