Estimation of P(X > Y ) for Weibull distribution based on hybrid censored samples

TL;DR

This paper develops methods to estimate the probability that one Weibull-distributed variable exceeds another using hybrid censored samples, providing estimators, confidence intervals, and Bayesian approaches with simulation validation.

Contribution

It introduces maximum likelihood, approximate MLE, and Bayesian estimators for P(X > Y) under hybrid censoring, including confidence and credible intervals, with comprehensive simulation studies.

Findings

MLE and AMLE estimators are derived and analyzed.

Confidence and credible intervals are constructed and validated.

Simulation results demonstrate the effectiveness of proposed methods.

Abstract

A Hybrid censoring scheme is mixture of Type-I and Type-II censoring schemes. Based on hybrid censored samples, this paper deals with the in- ference on R = P(X > Y ), when X and Y are two independent Weibull distributions with different scale parameters, but having the same shape pa- rameter. The maximum likelihood estimator (MLE), and the approximate MLE (AMLE) of R are obtained. The asymptotic distribution of the maxi- mum likelihood estimator of R is obtained. Based on the asymptotic distribu- tion, the confidence interval of R can be derived. 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.