Talk:Beta-binomial distribution

message: 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 (talk • contribs) 13:55, 9 July 2009 (UTC)

message: This article begins thus:
: 
:: 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)
thread_title:  more flexible alternative??? 

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

message: 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)
thread_title:  Missing definition?  Under Bayesian section 

message: 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 (talk • contribs) 16:09, 28 March 2013 (UTC)
thread_title:  Poisson-binomial distribution? 

message: 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)
thread_title:  Formula for 3F2 function in CDF 

message: 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)
thread_title:  Cumulants 

message: The y-axis label on the CDF plot currently reads P{X >= k}. I think according to the definition of the CDF it should be P{X <= k} (less or equal instead of more or equal).  — Preceding unsigned comment added by 2A02:8109:8A80:320:BAAE:EDFF:FE72:4D8 (talk) 18:16, 1 October 2020 (UTC)
thread_title:  CDF and y-label