The compound product distribution; a solution to the distributional equation X=AX+1
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.04758
- arXiv:
- arXiv:1905.04758
- Bibcode:
- 2019arXiv190504758C
- Keywords:
-
- Statistics - Computation;
- Statistics - Applications;
- 39A50;
- 39A60;
- 62F10;
- 62F25;
- 60-08;
- 60C05;
- 39A60;
- G.3;
- G.2.3
- E-Print:
- 10 pages, 5 figures, one appendix