Skew Lomax Distribution, Parameter Estimation, Its Properties, and Applications

Abstract

In this paper, a three-parameter distribution called the ‘Skew-Lomax’ distribution is proposed, which is the special case of the Azzalini distribution to generalize the Lomax distribution. The Lomax distribution is also called Pareto type II distribution, which is a heavy-tailed continuous probability distribution for a non-negative random variable. The statistical properties of the proposed Skew-Lomax distribution, including mean, variance,  moments about the origin, cumulative distribution function, hazard rate function, quantile function, and the random number generation have been derived. Also, the method of maximum likelihood and the method of moment to estimate the parameters of this distribution have been proposed. Three real data sets have been used to illustrate the usefulness, flexibility, and application of the proposed distribution. The coefficient of determination, chi-square test statistics, and the sum of the square of error depicts that the proposed model is more flexible than the Lomax distribution.