Abstract
Two estimation problems are studied based on the general progressively censored samples, and the distributions from the inverted scale family (ISF) are considered as prospective life distributions. One is the exact interval estimation for the unknown parameter θ , which is achieved by constructing the pivotal quantity. Through Monte Carlo simulations, the average 90 % and 95 % confidence intervals are obtained, and the validity of the above interval estimation is illustrated with a numerical example. The other is the estimation of R = P ( Y < X ) in the case of ISF. The maximum likelihood estimator (MLE) as well as approximate maximum likelihood estimator (AMLE) is obtained, together with the corresponding R-symmetric asymptotic confidence intervals. With Bootstrap methods, we also propose two R-asymmetric confidence intervals, which have a good performance for small samples. Furthermore, assuming the scale parameters follow independent gamma priors, the Bayesian estimator as well as the HPD credible interval of R is thus acquired. Finally, we make an evaluation on the effectiveness of the proposed estimations through Monte Carlo simulations and provide an illustrative example of two real datasets.
Highlights
General progressive censoring plays a key role in the field of lifetime analysis
With Bootstrap methods, we propose two R-asymmetric confidence intervals, which have a good performance for small samples
We consider three reliability models based on inverse Weibull distribution (IWD), generalized inverse exponential distribution (GIED), and the Weibull distribution (i.e., WD, the CDF and probability density functions (PDF) are given below), respectively
Summary
General progressive censoring plays a key role in the field of lifetime analysis. It generalizes the progressive censoring scheme, which allows removing surviving units from a life test stage-by-stage and to some extent, resolves the time and money constraints (Sen, [1]). Considers the situation of general progressive Type-II right censoring (GPTIIC). The scheme of GPTIIC and distributions from ISF both play a vital role in life researches, not much attention has been paid to the situation when the samples are from ISF under GPTIIC. In this case, we consider the following two estimation problems. Balakrishnan et al [10] obtained interval estimation for Normal distribution in the case of progressive Type-II censoring. We conduct a study on the exact interval estimation of θ as well as the estimation of R for ISF under GPTIIC. We evaluate the effectiveness of the proposed estimations through Monte Carlo simulations and provide an illustrative example of two real datasets
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