Abstract
The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.
Highlights
In type I censoring, the life-testing experiment terminates at a predetermined time while, under type II censoring, the life-testing test stops once the observed failure units reach the predetermined number
We focus on the exponentiated half-logistic distribution
Assume that the adaptive type II progressive censored data come from an exponentiated half-logistic distribution
Summary
In this day and age, owing to the development of science and technology, industrial products have become greatly reliable and as a result, getting sufficient failure time during a life testing experiment for any statistical analysis purposes results in a sharp increase in cost and time. For the sake of further reducing the experimental cost and time, a concoction of these two schemes called hybrid censoring was put forward None of these schemes permits the survival units to be removed during the experiment, which lacks flexibility. The half logistic distribution has extensive use employed in censored data in the area of survival analysis. The generalized ranked-set sampling technique was employed for obtaining parameters estimation of the half-logistic distribution in [12]. The problem of the point and interval estimation of the parameters for exponentiated half logistic distribution under adaptive type II progressive censored data are considered. Maximum likelihood estimation is used to estimate the unknown parameters on the basis of the adaptive type II progressive censored data. Assume that the adaptive type II progressive censored data come from an exponentiated half-logistic distribution. The Newton–Raphson method is employed to acquire the MLEs, written as σand λ
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