Pareto distribution - Maple Help

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Statistics[Distributions][Pareto] - Pareto distribution

 Calling Sequence Pareto(a, c) ParetoDistribution(a, c)

Parameters

 a - location parameter c - shape parameter

Description

 • The Pareto distribution is a continuous probability distribution with probability density function given by:

$f\left(t\right)=\mathrm{piecewise}\left(t

 subject to the following conditions:

$0

 • Note that the Pareto command is inert and should be used in combination with the RandomVariable command.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$
 > $X:=\mathrm{RandomVariable}\left(\mathrm{Pareto}\left(a,c\right)\right):$
 > $\mathrm{PDF}\left(X,u\right)$
 ${{}\begin{array}{cc}{0}& {u}{<}{a}\\ \frac{{c}{}{{a}}^{{c}}}{{{u}}^{{c}{+}{1}}}& {\mathrm{otherwise}}\end{array}$ (1)
 > $\mathrm{PDF}\left(X,0.5\right)$
 ${{}\begin{array}{cc}{0.}& {0.5}{<}{a}\\ \frac{{c}{}{{a}}^{{c}}}{{{0.5}}^{{c}{+}{1.}}}& {\mathrm{otherwise}}\end{array}$ (2)
 > $\mathrm{Mean}\left(X\right)$
 ${{}\begin{array}{cc}{\mathrm{undefined}}& {c}{\le }{1}\\ \frac{{c}{}{a}}{{-}{1}{+}{c}}& {\mathrm{otherwise}}\end{array}$ (3)
 > $\mathrm{Variance}\left(X\right)$
 ${{}\begin{array}{cc}{\mathrm{undefined}}& {c}{\le }{2}\\ \frac{{c}{}{{a}}^{{2}}}{{\left({-}{1}{+}{c}\right)}^{{2}}{}\left({-}{2}{+}{c}\right)}& {\mathrm{otherwise}}\end{array}$ (4)