Dagum Distribution: Properties and Different Methods of Estimation

Abstract

This article addresses the various properties and different methods of estimation of the unknown parameters of a three-parameter Dagum distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view, yet, various mathematical and statistical properties of the Dagum distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean past lifetime, mean deviation about mean and median,  various entropies, Bonferroni and Lorenz curves and order statistics) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, maximum product of spacings estimators,  minimum distances estimators, Cram\'{e}r-von-Mises estimators, Anderson-Darling and right-tail Anderson-Darling estimators and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, a real data set have been analyzed for illustrative purposes.