# Talk:Beta-binomial distribution

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I think this page would be much more helpful if it looked like the Beta distribution article, the Binomial distribution article and all other probability distribution articles. It wasn't clear what the pdf is etc, the mean, variance, kurtosis etc. Instead, the article read like a page in a Bayesian theory textbook.

I concur with the above suggestions. Also would like to know more about alternative estimation methods, including maximum likelihood and particularly Bayesian estimatation, either analytic closed-form solutions or numerical integration. —Preceding unsigned comment added by GradualStudent (talkcontribs) 13:55, 9 July 2009 (UTC)

## more flexible alternative???

In probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions used as a more flexible alternative to the binomial distribution.

Huh???

That is silly. Clearly it needs to get rewritten. I'd replace it right now if I could do so in a few seconds. Michael Hardy (talk) 21:09, 24 May 2010 (UTC)

I notice that the article begins differently now. I assume this is no longer an issue? If so, this section of the Talk page should be deleted... Insurrectionist (talk) 01:55, 17 July 2013 (UTC)

## How s^2 is determined? (in the section "Further Bayesian considerations")

In the section "Further Bayesian considerations", I see the following equation. But there is no derivation showing why this should be the estimate. I'd think the estimate should be different depending on different assumptions. I'm not who the original author of this equation is. Could anybody let me know how this equation is derived or how to contact the original author? Thanks.

$s^2 = \frac{N \sum_{i=1}^N n_i (\hat{\theta_i} - \hat{\mu})^2 } {(N-1)\sum_{i=1}^N n_i }.$

Ypsd (talk) 22:41, 22 June 2011 (UTC)

## Missing definition? Under Bayesian section

Under: Further Bayesian considerations The image http://upload.wikimedia.org/wikipedia/en/math/b/6/f/b6f8a72c64520a2eb84cb3bdbd1ac0ad.png contains the conditional l(k|theta); which I don't see defined. It may be obvious, in fact I could do the division, but I am just learning about conjugate priors and could use an explicit definition. And some explanation. Rrogers314 (talk) 18:15, 29 April 2012 (UTC)

## What is the second sample moment?

The example refers to $m_2$ as the second sample moment. The current Wikipedia on moments refers to moments about some value. Is $m_2$ the second moment about the sample mean? (i.e. the standard biased estimator for the sample variance)? Is it the second moment about zero?

## Poisson-binomial distribution?

One can also think of the n parameter in the binomial distribution as being randomly drawn from a Poisson distribution. For n = 1 one has k = 0 or k = 1. For n = 0 one has only k = 0 with probabilty 1. How would be the probability distribution of this Poisson-binomial distribution? — Preceding unsigned comment added by Ad van der Ven (talkcontribs) 16:09, 28 March 2013 (UTC)

Tashiro (talk) 02:18, 19 August 2012 (UTC)

## Formula for 3F2 function in CDF

Hey, I noticed that the formula for the CDF has 3F2(a, b, k) and then the note on the formula says, "where 3F2(a,b,k) is the generalized hypergeometric function =3F2(1, α + k + 1, −n + k + 1; k + 2, −β − n + k + 2; 1)". Is that last argument really supposed to be 1 or is it supposed to be k ?? Wile E. Heresiarch (talk) 05:30, 10 April 2014 (UTC)

## Cumulants

Dear main authors, the following formulas might be incorporated in the article.

Mean:

$\mu = n\pi \!$

Variance:

$\sigma^2 = n\pi(1-\pi)[1+(n-1)\rho] \!$

Skewness:

$\gamma_1 = \left(1+\dfrac{2(n-1)\rho}{1+\rho}\right)\dfrac{1-2\pi}{\sigma} \!$

Excess kurtosis:

$\gamma_2 =\left(1-6\pi(1-\pi)+\dfrac{6n\rho(1+n\rho)}{(1+\rho)(1+2\rho)}\left[1-(5+\rho)\pi(1-\pi)\right]\right)\dfrac{1}{\sigma^2} \!$

Beware: the kurtosis formulas given are usually the kurtosis proper $\beta_2$, better use the excess kurtosis $\gamma_2=\beta_2 - 3$, because it is a normalized cumulant.

Source: Overdispersion models in SAS (they write $\rho^2$ instead of $\rho$).

I checked the formulas numerically on the computer, they should be correct.

Regards: Herbmuell (talk) 08:32, 16 July 2015 (UTC).