Morad Alizadeh

Generalizing distributions is important for applied statisticians and recent literature has sug- gested several ways of extending well-known distributions. We propose a new class of distri- butions called the Marshall-Olkin Burr X family, which yields flexible shapes for its density such as symmetrical, left-skewed, right-skewed and reversed-J shaped, and can have increas- ing, decreasing,constant, bathtub and upside-down bathtub hazard rates shaped. Some of its structural properties including quantile and generating functions, ordinary and incomplete moments, and mean deviations are obtained. One special model of this family, the Marshall- Olkin-Burr-Lomax distribution, is investigated in details. We also derive the density of the order statistics. The model parameters are estimated by the maximum likelihood method. For illustrative purposes, three applications to real life data are presented.