Some inference results on pr(x < y) in the bivariate exponential model

Abstract

This paper provides three different estimators for Pr(X < Y) when X and Y have a bivariate exponential distribution. The asymptotic variances of the three estimators are also derived. A test for the equality of the means of X and Y and confidence limits for the difference of the two means are presented. Our results are directly applicable in a reliability context with underlying bivariate exponential distribution.

Selecting the Better Component of a Bivariate Exponential Distribution

“…From Arnold [1] or Awad, Azzam and Hamdan [2], based on ni and nj, that is, we select X as the better component when nj < and select y when ni > nj. In this case, the problem is same as Example 6.4.3 of Gibbons, Olkin and Sobel [8].…”

Estimation ofP(Y<X) for Weibull Distribution Under Progressive Type-II Censoring

“…Since R represents a relation between the stress and strength of a system, it is popularly known as the stress-strength parameter of that system. Several authors have studied the problem of estimating R. The MLE of P Y < X , when X and Y have bivariate exponential distribution, has been considered by Awad et al (1981). Gupta and Gupta (1990) considered the estimation of P Y < X , when X and Y are multivariate normally distributed.…”

Statistical Testing Procedure for Assessing The Quality Performance of Exponentiated Weibull Products with The Lower Record Values

“…Many related literatures have been considered the problem for estimating of R, for example, estimation of P[X > Y] based on the exponential distribution (see Tong (1974Tong ( , 1977, Aminzadeh (1997), Baklizi and El-Masri (2004), Krishnamoorthy et al (2007)), bivariate exponential distribution (see Awad et al (1981) and Nadarajah and Kotz (2006)), Burr type X distribution (see Ahmad et al (1997) and Padgett (1998, 2001), Burr type III distribution (see Mokhlis (2005) and Shawky and Alkashkari (2007)), gamma distribution (see Constantine and Karson (1986) and Nadarajah (2005)), generalized exponential distribution (see Kundu and Gupta (2005) and Wong and Wu (2009)), Weibull distribution (see McCool (1991), Kundu and Gupta (2006), Abd and Mohamed (2008), Kundu and Raqab (2009), Krishnamoorthy and Lin (2010) and Amiri et al (2013)), exponentiated Gumbel distribution (see Kakade et al (2008)) and generalized Pareto distribution (see Rezaei et al (2010)). The theoretical and practical results on the theory and applications of the stress-strength relationships in industrial and economic systems during the last decades are collected and digested in Kotz et al (2003).…”