Abstract
In this paper, some estimators for the reliability function R(t) of Basic Gompertz (BG) distribution have been obtained, such as Maximum likelihood estimator, and Bayesian estimators under General Entropy loss function by assuming non-informative prior by using Jefferys prior and informative prior represented by Gamma and inverted Levy priors. Monte-Carlo simulation is conducted to compare the performance of all estimates of the R(t), based on integrated mean squared.
Highlights
The British Benjamin Gompertz (1825) reached to the law of geometrical progression pervades large portions of different tables of mortality for humans
A special case of Gompertz distribution knows as Basic Gompertz (BG) distribution will be assumed by letting that ζ = 1 which is given by the following probability density function [2]
We provide a Bayesian estimation method for R(t) of BG distribution, including noninformative and informative priors
Summary
The British Benjamin Gompertz (1825) reached to the law of geometrical progression pervades large portions of different tables of mortality for humans. The formula he derived was commonly called the Gompertz equation, which is a valuable tool in demography, reliability analysis, and life testing. It is widely used in Bayesian estimation as a conjugate prior in demonstrating individuals' mortality and actuarial chart and different scientific disciplines fields such as biological, Marketing Science, in network theory.
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