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.

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

$\mathrm{FisherInformation}\left(\mathrm{Normal}\left(\mathrm{\mu }\,\mathrm{\sigma }\right)\,1\,\mathrm{\mu }\right)$

$\frac{1}{{\mathrm{\sigma }}^2}$

$\mathrm{FisherInformation}\left(\mathrm{Normal}\left(\mathrm{\mu }\,\mathrm{\sigma }\right)\,1\,\mathrm{\sigma }\right)$

$\frac{2}{{\mathrm{\sigma }}^2}$