Inference of $R=P(Y<X)$ for two-parameter Rayleigh distribution based on progressively censored samples

TL;DR

This paper develops and compares various estimation methods for the probability R=P(Y<X) where Y and X are from two-parameter Rayleigh distributions, using censored samples, and evaluates their performance through simulations and real data.

Contribution

It introduces new estimators and confidence intervals for R based on censored samples, including Bayesian and bootstrap methods, and compares their effectiveness.

Findings

Bayesian estimator performs well in simulations.

Bootstrap confidence intervals are competitive with asymptotic ones.

Method shows good performance on real data sets.

Abstract

Based on independent progressively Type-II censored samples from two-parameter Rayleigh distributions with the same location parameter but different scale parameters, the UMVUE and maximum likelihood estimator of $R=P(Y<X)$ are obtained. Also the exact, asymptotic and bootstrap confidence intervals for $R$ are evaluated. Using Gibbs {sampling,} the Bayes estimator and corresponding credible interval for $R$ are obtained too. Applying Monte Carlo {simulations,} we compare the performances of the different estimation methods. Finally we make use of simulated data and two real data sets to show the competitive performance of our method.