| 二项分布熵的性质 |
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| 引用本文： | 丁勇.二项分布熵的性质[J].软件,2012(2):144-146,149. |
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| 作者姓名： | 丁勇 |
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| 作者单位： | 南京医科大学数学教研室 |
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| 摘 要： | 本文证明了二项分布的熵有如下性质:设X～B(n,p),对确定的n,当p<(1/2)时,熵随着p的增加而增大,当p>(1/2)时,熵随着p的增加而减少,当p=(1/2)时,熵达到最大值;对确定的p,熵随着n的增加而增加。对两个有相同n或p的二项分布,方差相等时,它们的熵也相等;方差较大的二项分布对应的熵也较大。
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| 关 键 词： | 概率论 二项分布 熵 方差 |
The Characters of Entropy of Binomial Distribution |
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| DING Yong.The Characters of Entropy of Binomial Distribution[J].Software,2012(2):144-146,149. |
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| Authors: | DING Yong |
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| Affiliation: | DING Yong (Deptartment.of Mathematics,Nanjing Medical University,Nanjing 210029) |
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| Abstract: | This paper discusses the characters of entropy of binomial distribution.Suppose n and p are the parameters in binomial distribution.For any certain n,when p<(1/2),the entropy will increase with p increases,when p>(1/2),the entropy will increase with p decreases,when p=(1/2),the entropy achieves its maximum value.For any certain p,the entropy will increase with n increases.For two binomial distribution which have equalized n or p,equalized variance will lead to the same entropy,bigger variance will lead to larger entropy. |
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| Keywords: | Probability theoty Binomial distribution Entropy Variance |
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