A Proportional Hazard Marshall–Olkin Extended Family of Distributions and its Application to Gompertz Distribution

Abstract

In this paper, we have presented a proportional hazard version of the Marshall–Olkin extended family of distributions. This family of distributions has been compared in terms of stochastic orderings with the Marshall-Olkin extended family of distributions. Considering the Gompertz distribution as the baseline, the monotonicity of the resulting failure rate is shown to be either increasing or bathtub, even though the Gompertz distribution has an increasing failure rate. The maximum likelihood estimation of the parameters has been studied and a data set, involving the serum–reversal times, has been analyzed and it has been shown that the model presented in this paper fit better than the Gompertz or even the Mrashall–Olkin Gompertz distribution. The extension presented in this paper can be used in other family of distributions as well.

Keywords:

• Failure rate function
• Mean residual life function
• Order statistics
• Stochastic comparisons

Mathematics Subject Classification:

• Primary 62F10
• 62F12
• Secondary 60E05