Bayesian and Non - Bayesian Inference for Shape Parameter and Reliability Function of Basic Gompertz Distribution

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

Numerical Comparison by using Some Criteria to Estimate the Two Parameters of the Exponentiated Exponential Distribution

“…3. From Tables (6) and (7), MLM give the best performance in comparison with other Bayes estimates for estimating the shape parameter 𝓅 (with non-informative priors (𝔪 = 𝑣 =0.00001)) and with informative priors (𝔪 = 𝑣 =2) with all criteria and for all sample sizes. 4.…”

“…Bayes estimation of any function of the parameter ℎ(𝓅, 𝓆) under scale invariant squared error (SIS) ,can be obtained by the following expression, [6]:…”

Estimating Reliability for Frechet (3+1) Cascade Model

“…At the beginning of the twentieth century, interest in industrial machines increased and developed rapidly. Their complexity increased and it became impossible to do without them, so attention was increased to to the reliability of these machines and industrial models to avoid their downtime and loss of time [1][2][3]. Reliability is simply defined as the working time of the component and can be found using the function R = pr (X < Y ) [4,5], where X stands for the random variable of strength and Y stands for the random variable of stress [6,7], where the strength of the component resists stress and if the stress is greater than the strength the component stops working [8][9][10].…”