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

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  • Abt, Markus

Abstract

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.

Suggested Citation

  • Abt, Markus, 1994. "On the product and the sum of random variables with arithmetic and non-arithmetic distributions," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 291-297, March.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:4:p:291-297
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