A generalization of Lemma 1 in Kotlarski (1967)

Siran Li and Xunjie Zheng

Statistics & Probability Letters, 2020, vol. 165, issue C

Abstract: Kotlarski (1967) establishes a fundamental result on identification of marginal distributions of independent random variables X, Y, and Z from the joint distribution of random variables (U,V), where (U,V)=(X+Z,Y+Z). We extend this result to the case (U,V)=(X+aZ1+bZ2,Y+cZ1+dZ2), where Z1 and Z2 are identically distributed, and a, b, c, and d are different weights. As an outgrowth of the proof, we also present a complete solution to a generalized version of Cauchy functional equation.

Keywords: Kotlarski’s Lemma; Factor model; Cauchy functional equation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2020.108814

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