A New Family of Upper-Truncated Distributions: Properties and Estimation

Abstract

In this paper, a new truncated distribution related to Lomax distribution is introduced. The proposed distribution is referred to as upper-truncated Lomax distribution. Our purpose in this study includes introducing a new family of probability distributions based on the new [0,1] truncated Lomax distribution.  Statistical properties of the [0,1] truncated Lomax-G family like; moments, moment generating function, probability weighted moments, quantile function, order statistics and Rényi entropy are derived. Some sub-models of the family like; truncated Lomax-uniform, truncated Lomax-linear failure rate, truncated Lomax-Frѐchet and truncated Lomax-power function distributions are discussed. We discuss the estimation of the model parameters via maximum likelihood method in case of complete and censored samples. Furthermore, a simulation study is provided to evaluate the validity of maximum likelihood estimates for one sub-model. Finally, analysis of real data set, representing the breaking stress of carbon fibers, is conducted to demonstrate the usefulness of truncated Lomax-Frѐchet distribution compared with some competitor distributions.