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Haight [1] lists the “binomials added distribution” as a single entry without a formula:

MR17 refers to *Mathematical reviews*, which Haight notes as “in no case offer a review of a paper appearing in coded journals” and indicating “…publications in **obscure **(from the point of view of [1951]) sources.” The journal [w] referenced is *Mitteilungsblatt fur Mathematische Statistik*, Volume 5. I was unable to locate copies of either of these obscure references. If anyone has access, please leave a comment. Thank you!

The problem of adding binomials was addressed briefly in [2], referencing a formula for a toric ideal:

Carlini and Rapallo note that “the two added binomials do not have a simple statistical counterpart”.

This may indicate that adding certain binomials may be difficult to compute or intractable in some circumstances. Which may be why the “added binomials distribution” has vanished into obscurity.

**References**

[1] Haight, F. (1958). Index to the Distributions of Mathematical Statistics. National Bureau of Standards Report.

[2] Carlini, E. & Rapallo, F. (2013). Toric ideals with linear components: an algebraic interpretation of clustering the cells of a contingency table. Online: https://arxiv.org/pdf/1309.7622.pdf