\begin{definition}[Definition:Pareto Distribution]
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X \in \hointr b \infty$.
$X$ is said to have a '''Pareto distribution''' {{iff}} it has probability density function: 
:$\ds \map {f_X} x = \dfrac {a b^a} {x^{a + 1} }$
for $a, b \in \R_{> 0}$.
\end{definition}