A New Generalization of the Exponentiated Pareto Distribution With an Application

SYNOPTIC ABSTRACT

We introduce for the first time a new lifetime distribution, namely, transmuted exponentiated Pareto (TEP) distribution, which generalizes the exponentiated Pareto distribution proposed by Gupta, Gupta, and Gupta (1998) with an additional parameter using the quadratic rank transmutation map which was studied by Shaw and Buckley (2009) to provide greater flexibility in modeling data from a practical point of view. In this article, our main focus is on estimation from a frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefly describe different estimation procedures, namely, the method of maximum likelihood estimation, moment estimation, L-moment estimation, least square and weighted least squares estimation, maximum product of spacings estimation, and Cramér-von-Mises estimation. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of one real data set.

KEY WORDS AND PHRASES:

• Hazard rate function
• maximum likelihood estimation
• method of maximum product spacing
• transmuted exponentiated Pareto distribution