A generalization of Lemma 1 in Kotlarski (1967)
| Autor: | Xunjie Zheng, Siran Li |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Independent and identically distributed random variables Lemma (mathematics) Generalization 010102 general mathematics Cauchy functional equation 01 natural sciences Combinatorics 010104 statistics & probability Joint probability distribution 0101 mathematics Statistics Probability and Uncertainty Marginal distribution Random variable Mathematics |
| Zdroj: | Statistics & Probability Letters. 165:108814 |
| ISSN: | 0167-7152 |
| DOI: | 10.1016/j.spl.2020.108814 |
| Popis: | 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 + a Z 1 + b Z 2 , Y + c Z 1 + d Z 2 ) , where Z 1 and Z 2 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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