In mathematics, the term "characteristic function" can refer to any of several distinct concepts:
The indicator function of a subset, that is the function
which for a given subset A of X, has value 1 at points of A and 0 at points of X − A.
The characteristic function in convex analysis, closely related to the indicator function of a set:
In probability theory, the 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:
where denotes expected value. For multivariate distributions, the product tX is replaced by a scalar product of vectors.
The characteristic function of a cooperative game in game theory.
The characteristic polynomial in linear algebra.
The characteristic state function in statistical mechanics.
The Euler characteristic, a topological invariant.
The receiver operating characteristic in statistical decision theory.
The point characteristic function in statistics.
and 24 Related for: Characteristic function information
the term "characteristicfunction" can refer to any of several distinct concepts: The indicator function of a subset, that is the function 1 A : X → {...
In mathematics, an indicator function or a characteristicfunction of a subset of a set is a function that maps elements of the subset to one, and all...
current–voltage characteristic, the current in a circuit as a function of the applied voltage Receiver operating characteristicCharacteristic (algebra) of...
random variables with common characteristicfunction φ ( t ) {\displaystyle \varphi (t)} . The empirical characteristicfunction (ECF) defined as φ n ( t...
dependent scalar output (known as a transfer curve or characteristic curve). Transfer functions for components are used to design and analyze systems...
random variable X {\displaystyle X} is closely connected to the characteristicfunction φ X ( t ) {\displaystyle \varphi _{X}(t)} of that variable, which...
The characteristic state function or Massieu's potential in statistical mechanics refers to a particular relationship between the partition function of...
(t-2)t-1(-1)=t^{2}-2t+1\,\!,} the characteristic polynomial of A . {\displaystyle A.} Another example uses hyperbolic functions of a hyperbolic angle φ. For...
as a function p F ( m ) = χ ( X , F ( m ) ) {\displaystyle p_{\mathcal {F}}(m)=\chi (X,{\mathcal {F}}(m))} , where χ is the Euler characteristic of coherent...
equality, and of Pascal's rule in the second last equality. The characteristicfunction of each X k {\displaystyle X_{k}} and of Z {\displaystyle Z} is...
\end{aligned}}} The characteristicfunction is the Fourier transform of the probability density function. The characteristicfunction of the beta distribution...
_{j=1}^{n}e^{itx_{j}}} Knowing the characteristicfunction, it is possible to find the corresponding probability density function through the Fourier transform...
probability density function f X {\displaystyle f_{X}} of a scalar random variable X {\displaystyle X} is related to its characteristicfunction φ X {\displaystyle...
a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given...
its characteristicfunction (which uniquely determines the distribution) can be acquired by multiplying the corresponding characteristicfunctions. Consider...
})^{3}\,\pi (\lambda )\,d{\lambda }+\mu _{\pi }{\Biggr ]}.} The characteristicfunction has the form φ X ( s ) = M π ( e i s − 1 ) . {\displaystyle \varphi...
players N {\displaystyle N} , called the grand coalition, and a characteristicfunction v : 2 N → R {\displaystyle v:2^{N}\to \mathbb {R} } from the set...
Oskar Morgenstern's book.[citation needed] Formally, a characteristicfunction is a function v : 2 N → R {\displaystyle v:2^{N}\to \mathbb {R} } from...
cumulant-generating function as the natural logarithm of the characteristicfunction, which is sometimes also called the second characteristicfunction, H ( t )...
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the...
not periodic. The characteristicfunction of the wrapped exponential is just the characteristicfunction of the exponential function evaluated at integer...
and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the probability that a...
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