Science and Education Publishing American Journal of Modeling and Optimization 2333-1267 4 1 2016 5 3 Properties of the Distributions Generated by Mixing Weibull and Inverse Weibull Distributions with Zero Truncated Poisson 19 28 EN Salah H Abid Mathematics department, Education College, Al-Mustansiriya University, Baghdad, Iraq Sajad H Mohammed AJMO2016413 10.12691/ajmo-4-1-3 2015 12 10 2016 3 18 2016 5 1 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.