Paretovo rozdělení pravděbodobnosti

ATTENTION - instead of a decimal comma should be used decimal DOT ! (EN)

**सूत्र**
$P(x)=\begin{cases} \alpha\,\dfrac{x_\mathrm{m}^\alpha}{x^{\alpha+1}} & \text{for }x \ge x_\mathrm{m}, \\[12pt] 0 & \text{for } x < x_\mathrm{m}. \end{cases}$
$E(X)=\begin{cases} \infty & \text{if }\alpha\le 1, \\ \frac{\alpha x_\mathrm{m}}{\alpha-1} & \text{ }\alpha>1. \end{cases}$
$D(X)=\begin{cases} \infty & \text{ }\alpha\in(1,2], \\ \left(\frac{x_\mathrm{m}}{\alpha-1}\right)^2 \frac{\alpha}{\alpha-2} & \text{if }\alpha>2. \end{cases}$
$\gamma _{1}=\frac{2(1+\alpha)}{\alpha-3}\,\sqrt{\frac{\alpha-2}{\alpha}}\text{ }\alpha>3$
$\gamma _{2}=\frac{6(\alpha^3+\alpha^2-6\alpha-2)}{\alpha(\alpha-3)(\alpha-4)}\text{ }\alpha>4$