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Statistics

 FisherInformation
 Fisher information of a distribution

 Calling Sequence FisherInformation(R, N, U)

Parameters

 R - algebraic; a random variable or distribution N - algebraic, posint; number of samples U - symbol; a distribution parameter

Description

 • The FisherInformation function computes the Fisher information of a random variable or a distribution.  The Fisher information is defined as the amount of information conveyed towards the value of a distribution parameter in a particular sample.
 • The first parameter R can be a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
 • The second parameter N is an algebraic expression or positive integer which indicates the number of samples considered.
 • The third parameter U is a symbol which provides a parameter in the distribution for which the Fisher information should be calculated. For example, the distribution $\mathrm{Normal}\left(\mathrm{\mu },\mathrm{\sigma }\right)$ has two parameters ($\mathrm{\mu }$ and $\mathrm{\sigma }$) for which the Fisher information may be calculated.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$

Calculate the Fisher information of each term of the normal distribution.

 > $\mathrm{assume}\left(0<\mathrm{σ}\right)$
 > $\mathrm{FisherInformation}\left(\mathrm{Normal}\left(\mathrm{μ},\mathrm{σ}\right),1,\mathrm{μ}\right)$
 $\frac{{1}}{{{\mathrm{σ~}}}^{{2}}}$ (1)
 > $\mathrm{FisherInformation}\left(\mathrm{Normal}\left(\mathrm{μ},\mathrm{σ}\right),1,\mathrm{σ}\right)$
 $\frac{{2}}{{{\mathrm{σ~}}}^{{2}}}$ (2)