Talk:Poisson binomial distribution

I think the equations in the "Mean and variance" section only apply when n is large, for smaller values of n, a different distribution must be used. This is because of the LCLT. Getting this information from: (https://math.stackexchange.com/questions/2375886/approximating-poisson-binomial-distribution-with-normal-distribution) griffball (talk) Mon Apr 8 14:50:42 PDT 2019 —Preceding undated comment added 21:55, 8 April 2019 (UTC)[reply]

Sorry, I added wrong information about the entropy. Noticed right after adding. Already reversed the history. Rafael Calsaverini (talk) 17:17, 12 April 2011 (UTC)[reply]

In the DFT formula, what is i? Jim Bowery (talk) 14:46, 24 September 2011 (UTC).[reply]

I'm going to assume it is sqrt(-1) since this is a DFT, rather than an index as "i" is used in the prior formula. Jim Bowery (talk) 13:50, 25 September 2011 (UTC)[reply]

This paper http://arxiv.org/abs/1503.01570 seems to have proved Shepp-Olkin conjecture. — Preceding unsigned comment added by Wittawat (talk • contribs) 10:03, 8 April 2015 (UTC)[reply]

Could somebody change the title (I am not yet autoconfirmed) to "Poisson's binomial distribution"? I have seen more uses of the latter & it is more differentiating. — Preceding unsigned comment added by Nightspawn9911 (talk • contribs) 16:25, 24 March 2019 (UTC)[reply]

Google Ngram Viewer can't find any uses of the latter [1], so you must have unusual tastes in statistical literature. I don't understand what you mean by 'more differentiating'. If you wish to create a redirect I'd have no objection, however. --Qwfp (talk) 19:16, 24 March 2019 (UTC)[reply]

Asymptotic variance[edit]

The article says When the mean is fixed, the variance is bounded from above by the variance of the Poisson distribution with the same mean which is attained asymptotically as $n$ tends to infinity. I have my doubts: take for example $p_{i}=2^{-i}$ except $p_{n}=2^{-i+1}$ . Then $\mu =\sum p_{i}=1$ and is fixed, but the variance approaches ${\frac {2}{3}}$ as $n$ increases, which is not the $1$ of the corresponding Poisson distribution with the same mean. Perhaps I have misunderstood the claim. --Rumping (talk) 00:23, 31 July 2019 (UTC)[reply]

Mean and Variance, Probability Mass Function[edit]

I urge anyone who feels any kind of ownership of this page to define all variables that appear in formulas. It's not acceptable in any worthy publication to have formulas with undefined variables. For example, i, j, and A are not defined in these sections. Even if they're obvious to you, they should always be strictly defined. Chafe66 (talk) 00:12, 5 June 2020 (UTC)[reply]