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arXiv · 1905.04758

The compound product distribution; a solution to the distributional equation X=AX+1

Arrigo Coen
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Abstract

The solution of $ X=AX+1 $ is analyzed for a discrete variable $ A $ with $ \mathbb{P}\left[A=0\right]>0 $. Accordingly, a fast algorithm is presented to calculate the obtained heavy tail density. To exemplify, the compound product distribution is studied in detail for some particular families of distributions.

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Arrigo Coen. 2019-05-12. The compound product distribution; a solution to the distributional equation X=AX+1. https://arxiv.org/abs/1905.04758

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