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Characteristic function (probability theory)
In
probability theory
and
statistics
, the
characteristic function
of any
real-valued
random variable
completely defines its
probability distribution
. If a random variable admits a
probability density function
, then the characteristic function is the
inverse Fourier transform
of the probability density function. Thus it provides the basis of an alternative route to analytical results compared with working directly with
probability density functions
or
cumulative distribution functions
. There are particularly simple results for the characteristic functions of distributions defined by the weighted sums of random variables.
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