Abstract
In this paper, some estimators for the unknown shape parameters and reliability function of Basic Gompertz distribution were obtained, such as Maximum likelihood estimator and some Bayesian estimators under Squared log error loss function by using Gamma and Jefferys priors. Monte-Carlo simulation was conducted to compare the performance of all estimates of the shape parameter and Reliability function, based on mean squared errors (MSE) and integrated mean squared errors (IMSE's), respectively. Finally, the discussion is provided to illustrate the results that are summarized in tables.
Highlights
The Gompertz distribution plays an important role in modeling survival times, human mortality and actuarial data
We provide Bayesian estimation method for estimating and R(t) of Basic Gompertz distribution, including informative and non-informative priors
The discussion of the results obtained from applying the simulation study can be summarized as follows: 1. When the shape parameter =0.5, The best estimator for is Bayes estimator under quared log error loss function based on Gamma prior, with =0.8 and =3 for all sample sizes see Table-1)
Summary
The Gompertz distribution plays an important role in modeling survival times, human mortality and actuarial data. It was formulated by Gompertz (1825) to fit mortality tables[1]. The probability density function of the Gompertz distribution is defined as follows [2]:. Λ> 0 where c is the scale parameter and λ is the shape parameter of the Gompertz distribution. We’ll assume that c=1, which is a special case of Gompertz distribution known as. Tn are a random sample of size n from the Basic Gompertz distribution defined by eq(1), the likelihood function for the sample observation will be as follows [4].
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