Pareto random variable
$X$ is a Pareto random variable with parameters $a,b$ if
${f}_{X}(x)=\frac{a{b}^{a}}{{x}^{a+1}}$, $x\in [b,\mathrm{\infty})$
Parameters:

$\star $
$a\in (0,\mathrm{\infty})$

$\star $
$b\in (0,\mathrm{\infty})$
Syntax:
$X\sim Pareto(a,b)$
Notes:

1.
$X$ represents a random variable^{} with shape parameter $a$ and scale parameter $b$.

2.
The expected value^{} of $X$ is noted as $E[X]=\frac{ab}{a1}$ with $a\in \{2,3,\mathrm{\dots}\}$

3.
The variance^{} of $X$ is noted as $Var[X]=\frac{a{b}^{2}}{{(a1)}^{2}(a2)}$, $a\in \{3,4,\mathrm{\dots}\}$

4.
The cumulative distribution function^{} of $X$ is noted as $F(x)=1{(\frac{b}{x})}^{a}$

5.
The moments of $X$ around 0 are noted as $E[{X}^{n}]=\frac{a{b}^{n}}{an}$, $n\in \{1,2,\mathrm{\dots},a1\}$
Title  Pareto random variable 

Canonical name  ParetoRandomVariable 
Date of creation  20130322 12:34:05 
Last modified on  20130322 12:34:05 
Owner  alozano (2414) 
Last modified by  alozano (2414) 
Numerical id  9 
Author  alozano (2414) 
Entry type  Definition 
Classification  msc 62E15 
Synonym  Pareto distribution 