A new family of lifetime distributions with different directions of hazard rate

This paper introduces a new family of lifetime distributions with different directions of hazard rate due to compounding the Lomax with the generalized truncated geometric distributions. This family called the Lomax-Generalized Truncated Geometric Distribution (LGTG) with an integer number equals to the order statistics. The general and some special cases forms of the probability density, probability distribution, reliability and hazard rate functions as well as their properties are derived. The estimation of parameters is presented by simulation study. The application study is illustrated based on real data set.