IEVref: | 171-07-23 | ID: | |

Language: | en | Status: Standard | |

Term: | conditional entropy | ||

Synonym1: | mean conditional information content [Preferred] | ||

Synonym2: | average conditional information content [Admitted] | ||

Synonym3: | |||

Symbol: | $H\left(X|Y\right)$ | ||

Definition: | mean value of the conditional information content of the events in a finite set of mutually exclusive and jointly exhaustive events, given the occurrence of the events in another set of mutually exclusive and jointly exhaustive events $H(X|Y)={\displaystyle \sum _{i=1}^{n}{\displaystyle \sum _{j=1}^{m}p({x}_{i},{y}_{j})\cdot I({x}_{i}|{y}_{j})}}$ where $X=\left\{{x}_{1}\mathrm{,}\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}{x}_{n}\right\}$ is the set of events ${x}_{i}\left(i=\mathrm{1,}\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}n\right)$, $Y=\left\{{y}_{1}\mathrm{,}\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}{y}_{m}\right\}$ is the set of events ${y}_{j}\left(j=\mathrm{1,}\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}m\right)$, $I\left({x}_{i}|{y}_{j}\right)$ is the conditional information content of ${x}_{i}$ given ${y}_{j}$, and $p\left({x}_{i},{y}_{j}\right)$ the joint probability that both events occur | ||

Publication date: | 2019-03-29 | ||

Source | IEC 80000-13:2008, 13-32, modified – Addition of information useful for the context of the IEV, and adaptation to the IEV rules | ||

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Domain5: |

$H(X|Y)={\displaystyle \sum _{i=1}^{n}{\displaystyle \sum _{j=1}^{m}p({x}_{i},{y}_{j})\cdot I({x}_{i}|{y}_{j})}}$

where $X=\left\{{x}_{1}\mathrm{,}\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}{x}_{n}\right\}$ is the set of events ${x}_{i}\left(i=\mathrm{1,}\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}n\right)$, $Y=\left\{{y}_{1}\mathrm{,}\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}{y}_{m}\right\}$ is the set of events ${y}_{j}\left(j=\mathrm{1,}\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}m\right)$, $I\left({x}_{i}|{y}_{j}\right)$ is the conditional information content of ${x}_{i}$ given ${y}_{j}$, and $p\left({x}_{i},{y}_{j}\right)$ the joint probability that both events occur