Estimation of \(P(X>Y)\) for Weibull distribution based on hybrid censored samples
A hybrid censoring scheme is mixture of Type-I and Type-II censoring schemes. Based on hybrid censored samples, this paper deals with the inference on \(R = P(X>Y)\), when X and Y are two independent Weibull distributions with different scale parameters, but having the same shape parameter. The maximum likelihood estimator (MLE), and the approximate MLE of R are obtained. The asymptotic distribution of the MLE of R is obtained. Based on the asymptotic distribution, the confidence interval of R is constructed. Two bootstrap confidence intervals are also proposed. We consider the Bayesian estimate of R, and propose the corresponding credible interval for R. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a real data set has also been presented for illustrative purposes.
KeywordsApproximate maximum likelihood estimator Hybrid censoring Maximum likelihood estimator Stress-strength model
- Badar MG, Priest AM (1982) Statistical aspects of fiber and bundle strength in hybrid composites. In: Hayashi T, Kawata K, Umekawa S (eds) Progress in science and engineering composites. ICCM-IV, Tokyo, pp 1129–1136Google Scholar
- Efron B (1982) The jackknife, the bootstrap and other re-sampling plans. In: CBMSNSF regional conference series in applied mathematics 34, SIAM, Philadelphia, PAGoogle Scholar