Unbiased estimators of \(P(X<Y)\) and their variances in the case of uniform and two-parameter exponential distributions
type: Item
instance of: scholarly article
title: Unbiased estimators of \(P(X<Y)\) and their variances in the case of uniform and two-parameter exponential distributions
zbMATH Open document ID: 0863.62017
DOI: 10.1007/BF02362481
author: V. V. Ivshin
published in: Journal of Mathematical Sciences (New York)
publication date: 1997-05-21T00:00:00Z
review text: The statistical estimation of the probability of linear inequalities is widely used in practice. In particular, in reliability theory the problem is to estimate the probability of failure-free operation of a compound technical system. Let us assume that the system breaks down if the ``stress'' \(X\) exceeds the ``strength'' \(Y\). In this case, the terms ``stress'' and ``strength'' are understood in a wider meaning. If we assume that \(X\) and \(Y\) are independent random variables, then the probability of failure-free operation is \[ {\mathbf P}(X<Y).\tag{1} \] We consider the two-parameter exponential distribution with unknown shift and known scale parameters as well as the uniform distribution on a segment with one end known. For these cases unbiased estimators for (1) are found. We also obtain unbiased estimators for the variances of these unbiased estimators.
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 1011669
zbMATH Keywords: two-parameter exponential distribution
zbMATH Keywords: unknown shift
zbMATH Keywords: known scale
zbMATH Keywords: uniform distribution
zbMATH Keywords: unbiased estimators
zbMATH Keywords: variances
MaRDI profile type: Publication
cites work: Q3994679
cites work: On the estimation of \(Pr\{ Y<X\}\) for the two-parameter exponential distribution
description: scientific article; zbMATH DE number 1011669