Identification of the parameters of a trivariate normal vector by the distribution of the minimum

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• 作者：Elnaggar ; Mohamed ; Mukherjea ; Arunava
• 关键词：60E05 ; 62H05 ; Trivariate normal distributions ; Identification of parameters
• 刊名：Journal of Statistical Planning and Inference
• 出版年：1999
• 出版时间：May, 1999
• 年：1999
• 卷：78
• 期：1-2
• 页码：23-37
• 全文大小：130 K

文摘

This paper continues the work started by Basu and Ghosh (J. Multivariate Anal. 1978, 8, 413–429) and by Gilliland and Hannan (J. Amer. Statist. Assoc. 1980, 75 (371), 651– 654). Let X₁, X₂, X₃ be three random variables with joint distribution function . Here we consider the following problem: if Y₁, Y₂, Y₃ are another three random variables with joint distribution function such that min{X₁,X₂,X₃} and min{Y₁,Y₂,Y₃} have the same distribution, then how must and be related and must they be the same? This paper solves the problem when and are multivariate normal distributions such that ρ_ij, the correlation between X_i and X_j and ρ_ij′, the correlation between Y_i and Y_j are both independent of i and j. The problem is solved by identifying the parameters of uniquely in terms of the density of the minimum.