Abstract
In this paper, some estimators of the unknown shape parameter and reliability function of Basic Gompertz distribution (BGD) have been obtained, such as MLE, UMVUE, and MINMSE, in addition to estimating Bayesian estimators under Scale invariant squared error loss function assuming informative prior represented by Gamma distribution and non-informative prior by using Jefferys prior. Using Monte Carlo simulation method, these estimators of the shape parameter and R(t), have been compared based on mean squared errors and integrated mean squared, respectively
Highlights
The Gompertz distribution (GD) was originally introduced by Gompertz in1825 (1).This distribution is used in model survival times, modeling human mortality and actuarial tables
The simulation experiments results show a convergence between the expected values (EXP) to the true values of the parameter φ with an increase in the sample sizes
The Bayes estimator under Scale invariant squared error loss function with Gamma prior is the best estimator for the shape parameter in comparing to others, such that the value of the shape parameter of Gamma prior γ should be less than (1) for all cases and the value of the scale parameter of Gamma prior should be chosen greater than 1 if the shape parameter of Basic Gompertz distribution is less than 1 and vice versa
Summary
The Gompertz distribution (GD) was originally introduced by Gompertz in1825 (1).This distribution is used in model survival times, modeling human mortality and actuarial tables. Bayes estimator relative to (SISELF) based on Gamma prior, can be derived as follows
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