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- W2125898599 abstract "<para xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> It is shown that the <emphasis><formula formulatype=inline><tex>${hbox{Binomial}}(n, p)$</tex></formula></emphasis> distribution maximizes the entropy in the class of ultra-log-concave distributions of order <emphasis><formula formulatype=inline> <tex>$n$</tex></formula></emphasis> with fixed mean <emphasis><formula formulatype=inline> <tex>$np$</tex></formula></emphasis>. This result, which extends a theorem of Shepp and Olkin (1981), is analogous to that of Johnson (2007), who considers the Poisson case. The proof constructs a Markov chain whose limiting distribution is <emphasis><formula formulatype=inline><tex>${hbox{Binomial}}(n, p)$</tex> </formula></emphasis> and shows that the entropy never decreases along the iterations of this Markov chain. </para>" @default.
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- W2125898599 date "2008-07-01" @default.
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- W2125898599 title "On the Maximum Entropy Properties of the Binomial Distribution" @default.
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- W2125898599 doi "https://doi.org/10.1109/tit.2008.924715" @default.
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