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 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