Identification of the parameters of a trivariate normal vector by the distribution of the minimum
type: Item
instance of: scholarly article
title: Identification of the parameters of a trivariate normal vector by the distribution of the minimum
zbMATH Open document ID: 0928.62039
DOI: 10.1016/S0378-3758(98)00204-3
author: Mohamed Elnaggar
author: A. Mukherjea
published in: Journal of Statistical Planning and Inference
publication date: 2000-01-11T00:00:00Z
review text: In competing risks theory and reliability of multicomponent systems occurs the following type of problem (P): Let \(X_1\), \(X_2\), \(X_3\) be three random variables with joint distribution function \(F\), and \(Y_1\), \(Y_2\), \(Y_3\) another three random variables with joint distribution function \(G\). If \(\min \{X_1, X_2, X_3\}\) and \(\min \{Y_1, Y_2, Y_3\}\) have the same distribution, then how \(F\) and \(G\) should be related, and must they be the same? The main result of the present paper is to solve (P) when \(F\) and \(G\) are multivariate normal distributions such that the correlation \(\rho_{ij}\) between \(X_i\) and \(X_j\), and the corelation \(\rho_{ij}'\) between \(Y_i\) and \(Y_j\) are both independent of \(i\) and \(j\). The problem (P) is solved by identifying the parameters of \(F\) uniquely in terms of the density function for the random variable minimum.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62H20
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 1331383
zbMATH Keywords: trivariate normal distributions
zbMATH Keywords: identification of parameters
zbMATH Keywords: competing risks
zbMATH Keywords: reliability of multicomponent systems
MaRDI profile type: Publication
cites work: Q4157815
cites work: Q4179683
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cites work: The problem of identification of parameters by the distribution of the maximum random variable: Solution for the trivariate normal case
cites work: Mill's ratio for multivariate normal distributions
description: scientific article; zbMATH DE number 1331383