A Novel Lomax Extension with Statistical Properties, Copulas, Different Estimation Methods and Applications

Abstract

A new compound Lomax model is proposed and analyzed. The novel distribution is derived based on compounding the zero truncated Poisson distribution and the exponentiated exponential Lomax distribution. The new density can be “monotonically left skewed,” “monotonically right skewed” and “symmetric” with various useful shapes. The new hazard rate can be “upside down bathtub-increasing,” “bathtub (U-shape),” “monotonically decreasing,” “increasing-constant” and “monotonically increasing.” Relevant statistical properties are derived. We briefly describe different estimation methods, namely the maximum likelihood, Cramér-von-Mises, ordinary least squares, weighted least square, Anderson–Darling, right tail Anderson–Darling and left tail Anderson–Darling. Monte Carlo simulation experiments are performed for comparing the performances of the proposed methods of estimation for both small and large samples. For facilitating the mathematical modeling of the bivariate real data sets, we derive some new corresponding bivariate distributions. Graphical simulation study is performed for assessing the finite sample behavior of the estimators using the maximum likelihood method. Two applications are provided for illustrating the applicability of the new model.