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。
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.
出处
《软件》
2012年第2期144-146,149,共4页
Software
关键词
概率论
二项分布
熵
方差
Probability theoty
Binomial distribution
Entropy
Variance
