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For probability distributions which don't have an explicit density function expression, but have an explicit [[quantile function]] expression, <math>Q(p)</math>, then <math>h(Q)</math> can be defined in terms of the derivative of <math>Q(p)</math> i.e. the quantile density function <math>Q'(p)</math> as <ref>{{Citation |last1=Vasicek  |first1=Oldrich |year=1976 |title=A Test for Normality Based on Sample Entropy |journal=[[Journal of the Royal Statistical Society, Series B]] |volume=38 |issue=1 |jstor=2984828 |postscript=. }}</ref>{{rp|54–59}}

For probability distributions which don't have an explicit density function expression, but have an explicit [[quantile function]] expression, <math>Q(p)</math>, then <math>h(Q)</math> can be defined in terms of the derivative of <math>Q(p)</math> i.e. the quantile density function <math>Q'(p)</math> as <ref>{{Citation |last1=Vasicek  |first1=Oldrich |year=1976 |title=A Test for Normality Based on Sample Entropy |journal=[[Journal of the Royal Statistical Society, Series B]] |volume=38 |issue=1 |jstor=2984828 |postscript=. }}</ref>{{rp|54–59}}

  --[[用户:CecileLi|CecileLi]]([[用户讨论:CecileLi|讨论]])  【审校】此处缺无格式的英文及翻译 补充：

  --[[用户:CecileLi|CecileLi]]([[用户讨论:CecileLi|讨论]])  【审校】此处缺无格式的英文及翻译 补充：For probability distributions which don't have an explicit density function expression, but have an explicit quantile function expression, , then  can be defined in terms of the derivative of  i.e. the quantile density function as

:<math>h(Q) = \int_0^1 \log Q'(p)\,dp</math>.

:<math>h(Q) = \int_0^1 \log Q'(p)\,dp</math>.

A modification of differential entropy that addresses these drawbacks is the relative information entropy, also known as the Kullback–Leibler divergence, which includes an invariant measure factor (see limiting density of discrete points).

A modification of differential entropy that addresses these drawbacks is the relative information entropy, also known as the Kullback–Leibler divergence, which includes an invariant measure factor (see limiting density of discrete points).

针对这些缺点，微分熵的一个改进是相对熵，也被称为 Kullback-Leibler 分歧，其中包括一个不变测度因子(见离散点的极限密度)。

针对这些缺点的一个改进方法是相对熵，也被称为 Kullback-Leibler 分歧，其中包括一个不变测度因子(见离散点的极限密度)。