Inference under progressively type II right-censored sampling for certain lifetime distributions

In this article, estimation of the parameters of a certain family of two-parameter lifetime distributions based on progressively Type II right-censored samples (including ordinary Type II right censoring) is studied. This family, of proportional hazard distributions, includes the Weibull, Gompertz, and Lomax distributions. A type of parameter estimation named inverse estimation is investigated for both parameters. Exact confidence intervals for one of the parameters and generalized confidence intervals for the other are explored; inference for the first parameter can be accomplished by our methodology independently of the unknown value of the other parameter in this family of distributions. Derivation of the estimation method uses properties of order statistics. A simulation study concentrating mainly on the Weibull distribution illustrates the accuracy of these confidence intervals [and the shorter length of our exact confidence interval compared with an alternative of Wu (2002)] and compares inverse estimators favorably with maximum likelihood estimators. A numerical example is used to illustrate the proposed procedures