Conformable fractional Lomax probability distribution

Abstract

In this paper, we consider the conformable fractional Lomax distribution. The main functions associated to this new distribution are obtained, including conformable cumulative distribution function and hazard rate function. Further, we derive an exact expression of the 𝑟^𝑡ℎ moment, the mean and the variance of such new distribution. The mode and the quantile function related to this distribution are also obtained. Some entropy measures, namely, Shannon entropy and Renyi entropy are derived. Moreover, we introduce the order statistics of a fractional random variable, the density of the 𝑘^𝑡ℎ order statistic and the joint density of the 𝑘^𝑡ℎ and 𝑚^𝑡ℎ order statistics for the new distribution are obtained.