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

05/12/2019

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by   Arrigo Coen, et al.

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The solution of X=AX+1 is analyzed for a discrete variable A with P[A=0]>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.