On the product and the sum of random variables with arithmetic and non-arithmetic distributions

We show that the distribution of the product and the sum of independent random variables having arithmetic distributions is again arithmetic. In case of the product, it is also possible to give a formula for the span. Furthermore, we also prove the converse statement. If the distribution of the sum of the product of independent random variables is arithmetic, this already forces the distributions of the random variables itsself to be arithmetic.

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Year of publication:	1994
Authors:	Abt, Markus
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 19.1994, 4, p. 291-297
Publisher:	Elsevier
Keywords:	Arithmetic distribution span sum and product of independent random variables

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005259288