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

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 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 (AMLE) of R are obtained. The asymptotic distribution of the maximum likelihood estimator of R is obtained. Based on the asymptotic distribution, 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.

Bayesian estimation of $$R=P[Y<X]$$ for inverse Lomax distribution under progressive type-II censoring scheme

“…The estimation of SSR parameter based on record sample have also been discussed for the different probability distribution, see Raqab (2002), Baklizi (2007, Baklizi (2012), Hasan et al (2018) etc. Further, the estimation of SSR parameter for Weibull distribution has been studied by Asgharzadeh and Kundu (2015) using hybrid censored sample. The estimation of P½Y\X based on progressive censoring for Weibull distribution is studied by Asgharzadeh et al (2011), also for exponential distribution under progressive censoring is discussed by Saracoglua et al (2012).…”

The mean remaining strength of parallel systems in a stress-strength model based on exponential distribution

“…The last few decades, the problem of estimating R has been considerable investigated by many authors for the di¤erent data types and the distributional assumptions on X and Y . Examples of such results and references can be found in Kotz et al [3], Kundu and Gupta [4], Basirat et al [5,6], Asgharzadeh et al [7]. However, some results in the multicomponent stress-strength models can be found in Bhattacharyya and Johnson [8,9], Eryilmaz [10,11], Pakdaman and Ahmadi [12,13], Hassan [14], K¬z¬laslan [15].…”

Interval Estimation of Stress-Strength Reliability for a General Exponential Form Distribution with Different Unknown Parameters

“…Many authors have studied the interval estimation of R. Among them, (Kundu and Gupta, 2006), (Krishnamoorthy and Lin, 2010), (Asgharzadeh et al, 2011), and (Asgharzadeh et al, 2013). (Kotz et al, 2003) have comprehensively covered the problem of point and interval estimation of R. (Singh et al, 2015), and (Asgharzadeh et al, 2017) have also discussed the problem of point and interval estimation of R. Recently, (Mokhlis et al, 2017) introduced point and interval estimation of R = P (X 1 <X 2 ) by different methods when X 1 and X 2 follow a general exponential form or a general inverse exponential form with survival functions given by either…”