The Pareto distribution is a power distribution which was initially invented to describe the distribution of income but has found application in many other areas.
The Pareto distribution was developed in the late 19th century by Italian economist Vilfredo Pareto to describe the allocation of income and wealth among individuals. The distribution has found application in many other areas such as computing science, civil engineering, stock markets, physics, astronomy or insurance.
Its pdf is given by:
$$ f(x|a,b) = \frac{ba^b}{x^{b+1}} $$
for $x \geq a > 0$ and $b>0$, where $a$ provides the lower bound that a Pareto distributed random variable can take whilst $b$ determines the heaviness of the right tail.
The first two moments are:
\begin{align} &\text{mean: }& &\frac{ab}{b-1} \\[7pt] &\text{variance (when }b>2\text{): }& &\frac{ba^2}{(b-1)^2(b-2)} \end{align}
