On a characterization of probability distribution based on maxima of independent or max-independent random variables

2024/07/14 by Б. Л. С. Пракаса Рао, Rao, B. L. S. Prakasa
Computer Science · #62E10 #FOS: Mathematics #Neural Networks and Applications #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2407.10111

openalex publication_date 2024/07/14 · openalex created_date 2024/07/17 · openalex updated_date 2026/07/28

Abstract

Kotlarski (1978) proved a result on identification of the distributions of independent random variables X,Y and Z from the joint distribution of the bivariate random vector (U,V) where (U,V)= (max(X,Z),max(Y,Z)). We extend this result to the case (U,V)=(max(X,aZ₁,bZ₂),max(Y,cZ₁,dZ₂)) where X,Y,Z₁,Z₂ are independent or max-independent random variables, Z₁ and Z₂ are identically distributed and a,b,c,d are known positive constants.

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