Poisson binomial distribution: Difference between revisions

Revision as of 13:11, 26 August 2020

Revision as of 02:34, 31 August 2020

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| doi = 10.1109/TAES.2010.5461658

| bibcode = 2010ITAES..46..803F

| s2cid = 1456258

}}

</ref>

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|year = 1981

|mr = 0618689

|url = https://books.google.co.ukcom/books?id=9qziBQAAQBAJ

|isbn = 0-12-274460-8

}}</ref> This conjecture was proved by Erwan Hillion and Oliver Johnson in 2015.<ref>{{Cite journal |lastlast1=Hillion|firstfirst1=Erwan|last2=Johnson|first2=Oliver|date=2015-03-05|title=A proof of the Shepp-Olkin entropy concavity conjecture |journal=Bernoulli|volume = 23|issue=4B|pages = 3638–3649 | arxiv=1503.01570 |doi=10.3150/16-BEJ860|s2cid=8358662}}</ref> The Shepp-Olkin monotonicity conjecture, also from the same 1981 paper, is that the entropy is monotone increasing in <math>p_i</math>, if all <math>p_i \leq 1/2</math>. This conjecture was also proved by Hillion and Johnson, in 2019 <ref>{{Cite journal |lastlast1=Hillion|firstfirst1=Erwan|last2=Johnson|first2=Oliver|date=2019-11-09|title=A proof of the Shepp-Olkin entropy monotonicity conjecture |journal=Electronic Journal of Probability| volume = 24 |number=126 | pages = 1-141–14 |doi=10.1214/19-EJP380|doi-access=free}}</ref>

==Chernoff bound==