Characteristic function: Difference between revisions

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Revision as of 14:10, 5 March 2015

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:which for a given subset ''A'' of ''X'', has value 1 at points of ''A'' and 0 at points of ''X'' − ''A''.

* In probability theory, the [[characteristic function (probability theory) | characteristic function]] of any probability distribution on the real line is given by the following formula, where ''X'' is any random variable with the distribution in question:

::<math>\varphi_X(t) = \operatorname{E}\left(e^{itX}\right)</math>,

:where E means expected value. This concept extends to multivariate distributions.

* The [[characteristic function (convex analysis) | characteristic function]] in convex analysis:

::<math>\chi_{A} (x) := \begin{cases} 0, & x \in A; \\ + \infty, & x \not \in A. \end{cases}</math>

* The [[cooperative game]] in game theory.

* The [[characteristic state function]] in statistical mechanics.

* The [[characteristic polynomial]] in linear algebra.

* The [[characteristic state function]] in statistical mechanics.

* The [[Euler characteristic]], a topological invariant.

* The [[cooperative game]] in game theory.

* The [[Receiver operating characteristic]] in statistical decision theory.

* The [[point characteristic function]] in statistics.

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