characteristic function
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In mathematics,
characteristic function can refer to any of several distinct concepts:
- The most common and universal usage is as a synonym for indicator function, that is the function
which for every subset
A of
X, has value 1 at points of
A and 0 at points of
X −
A.
*When applied to a natural number an effective procedure determines correctly if a natural number is or is not in the procedure's "set": "The
characteristic function is the function that takes the value 1 for numbers in the set, and the value 0 for numbers not in the set" (cf Boolos-Burgess-Jeffrey (2002) p. 73).
χA (x) := beg∈cases 0 & x ∈ A; + &∈f∈; & x not ∈ A. endcases
- In probability theory, the characteristic function (probability theory) 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:
var&(hi;X(t) = E((eitX&nbs(;))
where E means expected value. This concept extends to multivariate distributions.
{{disambig}}
Charakteristische FunktionFunzione caratteristicaFunkcja charakterystyczna
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- time: 1:51pm EDT - Thu, Mar 18 2010
