Bayesian Approximation Techniques for Gompertz Distribution

Abstract

We presented approximate to Bayesian integrals of Gompertz distribution depending upon numerical integration and simulation study and showed how to study posterior distribution by means of simulation study. From the findings of above tables (1, 2, 3, 4) it has been found that the large sample distribution could be improved when prior is taken into account. In all cases (simulated data as well as real life data) normal approximation, T-K approximation, Bayesian estimates under informative priors are better than those under non-informative priors especially the Inverse levy distribution proves to be efficient with minimum posterior standard deviation. Further we accomplish that the posterior standard deviation based on different priors tends to decrease with the increase in sample size. It indicates that the estimators attained are consistent. It can also be detected that the performance of Bayes estimates under informative priors (inverse levy) is better than non-informative prior.

Bayesian Approximation Techniques for the Generalized Inverted Exponential Distribution

“…Therefore, many approximation procedures are used to evaluate Bayesian estimators. Shawky et al [15], Singh et al [16], Sultan et al [17,18], and Fatima et al [19] discuss some approximation approaches as the Lindley's, Tierney and Kadane's (T-K), and normal approximation methods to compute the Bayesian estimators of the exponentiated Gamma, Marshall-Olkin extended exponential, Kumaraswamy, Topp-Leone, and inverse exponential distributions, respectively. So, in this article, we use normal, Lindley's, and Tierney and Kadane's approximation methods to derive Bayesian estimators for the shape parameter of GIED in Sections 2 and 3.…”