An extended Lomax distribution

Abstract

A new five-parameter continuous distribution, the so-called McDonald Lomax distribution, that extends the Lomax distribution and some other distributions is proposed and studied. The model has as special sub-models new four- and three-parameter distributions. Various structural properties of the new distribution are derived, including expansions for the density function, explicit expressions for the moments, generating and quantile functions, mean deviations and Rényi entropy. The score function is derived and the estimation is performed by maximum likelihood. We also obtain the observed information matrix. An application illustrates the usefulness of the proposed model.

Keywords:

• Lomax distribution
• McDonald distribution
• maximum-likelihood estimation
• mean deviation
• Pareto type II distribution

Acknowledgements

We thank an anonymous referee and an associate editor for helpful suggestions. We gratefully acknowledge grants from FAPES and CNPq (Brazil).