Two New Lifetime Distributions of X-Weibull Family: Theories and Applications

In this paper, two new distributions, weibull-rayleigh and weibull-exponential of X —weibull family are introduced. The various properties of theses distributions, for example, the density functions, distribution functions, hazard rate functions, moment functions and Shannon entropy are investigated and capabilities of distributions compared to other distributions. Also by using simulation from these two distributions with various parameters some of the sample statistical indexes are estimated. Two real data sets are used to illustrate the applicability of these distributions.