Generalization of Gompertz Distribution and its Applications in Reliability and Time series

Generalization of Gompertz Distribution

Abstract

In this paper, as a generalization of the Gompertz distribution, Marshall-
Olkin Gompertz distribution is considered. A three parameter AR(1) process is also considered. When X and Y are two independent random variables following Marshall Olkin Gompertz distribution, then average bias, average mean square error, average confidence length and coverage probability of the of the simulated estimates of reliability R is computed. Data analysis based on a real data set and modeling are also done.