Talk:Negative hypergeometric distribution

The PDF formula refers to the parameter n, which is undefined. This is probably a typo. --Erel Segal (talk) 15:15, 23 March 2015 (CET)

Typo, indeed. It should be $N$, not $n$. Thank you. Would you like to fix it yourself? --Boris Tsirelson (talk) 18:08, 23 March 2015 (CET)

The equation was an image I could not edit, so I replaced it with a latex equation - I hope I did this right. --Erel Segal (talk) 20:31, 24 March 2015 (CET)

Yes, this is one of our problems; you could look at Help:HowTo EoM, or just see some new articles made in TeX. Anyway, I did it a bit nicer. Boris Tsirelson (talk) 08:17, 25 March 2015 (CET)

Yes, this looks much nicer. While we are at it: I did not understand why this formula is correct. Can you please add an intuitive explanation? Also, I didn't understand the formula at the bottom, connecting the negative-hypergeometric with the hypergeometric. Can you explain this too? --Erel Segal (talk) 08:25, 25 March 2015 (CET)

Wow... not now, maybe later. Boris Tsirelson (talk) 08:30, 25 March 2015 (CET)

The PMF formula (*) is suspicious. If m<N, then k+m-N<k, so the top-left factor is zero! --Erel Segal (talk) 19:23, 25 March 2015 (CET)

Some sources available:

• planetmath;
• N. Balakrishnan, V.B. Nevzorov, "A primer on statistical distributions", Wiley 2004 (see page 103);
• Shaughnessy;
• Mansuri

Boris Tsirelson (talk) 20:45, 26 March 2015 (CET)

Hmmm... After rewriting the three formulas in the last three sources in terms of EoM I got, respectively, \[ \frac{ {k+m-1 \choose k}{N-m-k \choose M-m} } { {N \choose M} } \, ; \] \[ \frac{ {M \choose k-1}{N-M \choose m} } { {N \choose m+k-1} } \cdot \frac{ M-k+1 }{ N-m-k+1 } \; , \] \[ \frac{ {k+m-1 \choose k-1}{N-m-k \choose M-m} } { {N \choose M} } \, . \] I am puzzled. Boris Tsirelson (talk) 21:43, 26 March 2015 (CET)