# Pareto distribution Calculator

## Calculates the probability density function and lower and upper cumulative distribution functions of the pareto distribution.

 percentile x scale parameter xm shape parameter α 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Pareto\ distribution\\[10](1)\ probability\ density\\\hspace{30}f(x,x_{m},\alpha)={\large\frac{\alpha x_{m}^{\alpha}}{x^{\alpha + 1}}}\\(2)\ lower\ cumulative\ distribution\\\hspace{30}P(x,x_{m},\alpha)={\large\int_{\hspace{15}\small x_{m}}^{\hspace{25}\small x}}f(x,x_{m},\alpha)dx={\large 1 - \left( \frac{x_{m}}{x} \right)^{\alpha} }\\(3)\ upper\ cumulative\ distribution\\\hspace{30}Q(x,x_{m},\alpha)={\large\int_{\hspace{5}\small x}^{\hspace{25}\small \infty}}f(x,x_{m},\alpha)dx={\large \left( \frac{x_{m}}{x} \right)^{\alpha} }\\$
Pareto distribution
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