Properties and Applications of a New Member of the T-X Family of Distributions

Abstract

In this paper, we introduce a new family of distributions by the use of the so-called T-X transformation defined with the Weibull distribution as generator and a sophisticated transformation involving logarithmic and power functions. We motivate the interest of this family in the fields of probability and statistics by complete theoretical and practical studies. Our theoretical investigations show how the family can be handle analytically, with formula for moments, moment generating function and order statistics. Then, the applied side is considered with a special focus on the member based on the so-called Lomax distribution. The motivation behind this member is to define a new five parameter lifetime distribution having a very flexible probability density function. We apply the related model by the means of two well-known real-life data sets, showing that the new distribution fits better than seven recent competitors.