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→Relation to estimator error
:<math>\operatorname{E}[(X - \widehat{X})^2] \ge \frac{1}{2\pi e}e^{2h(X)}</math>
:<math>\operatorname{E}[(X - \widehat{X})^2] \ge \frac{1}{2\pi e}e^{2h(X)}</math>
with equality if and only if <math>X</math> is a Gaussian random variable and <math>\widehat{X}</math> is the mean of <math>X</math>.
with equality if and only if <math>X</math> is a Gaussian random variable and <math>\widehat{X}</math> is the mean of <math>X</math>.
--[[用户:CecileLi|CecileLi]]([[用户讨论:CecileLi|讨论]]) 【审校】补充翻译：
==与估计器误差的关系==
微分熵给出了[[估计量]]的期望平方误差的下界。对于任何随机变量<math>X</math>和估计器<math>\widehat{X}</math>来说，以下条件成立：<ref name=“cover\u thomas”/>
：<math>\operatorname{E}[（X-\widehat{X}）^2]\ge\frac{1}{2\pi E}E^{2h（X）}</math>
当且仅当<math>X</math>是高斯随机变量，<math>\widehat{X}</math>是<math>X</math>的平均值。
==Differential entropies for various distributions==
==Differential entropies for various distributions==