The extended Burr XII distribution: properties and applications

Abstract

This paper introduces a new four-parameter lifetime model called the Marshall-Olkin generalized Burr XII (MOGBXII) distribution. We derive some of its mathematical properties, including quantile and generating functions, ordinary and incomplete moments, mean residual life, and mean waiting time and order statistics. The MOGBXII density can be expressed as a linear mixture of Burr XII densities. The maximum likelihood and least squares methods are used to estimate the MOGBXII parameters. Simulation results are obtained to compare the performances of the two estimation methods for both small and large samples. We empirically illustrate the flexibility and importance of the MOGBXII distribution in modeling various types of lifetime data.