Minimum variance unbiased estimation in the Gompertz distribution under progressive type II censored data with binomial removals (Q1952696)

Summary: This paper deals with the problem of uniformly minimum variance unbiased estimation for the parameter of the Gompertz distribution based on progressively Type II censored data with binomial removals. We have obtained the uniformly minimum variance unbiased estimator (UMVUE) for powers of the shape parameter and its functions. The UMVUE of the variance of these estimators is also given. The UMVUE of (i) pdf, (ii) cdf, (iii) reliability function, and (iv) hazard function of the Gompertz distribution is derived. Further, an exact \((1 - \alpha)\)100\% confidence interval for the \(p\)th quantile is obtained. The UMVUE of pdf is utilized to obtain the UMVUE of \(P(X < Y)\). An illustrative numerical example is presented.