# 帕累托分布

参数 概率密度函數 累積分布函數 xm > 0 k > 0 ${\displaystyle x\in [x_{\mathrm {m} };+\infty )\!}$ ${\displaystyle {\frac {k\,x_{\mathrm {m} }^{k}}{x^{k+1}}}\!}$ ${\displaystyle 1-\left({\frac {x_{\mathrm {m} }}{x}}\right)^{k}\!}$ ${\displaystyle {\frac {k\,x_{\mathrm {m} }}{k-1}}\!}$，${\displaystyle k>1}$ ${\displaystyle x_{\mathrm {m} }{\sqrt[{k}]{2}}}$ ${\displaystyle x_{\mathrm {m} }\,}$ ${\displaystyle {\frac {x_{\mathrm {m} }^{2}k}{(k-1)^{2}(k-2)}}\!}$，${\displaystyle k>2}$ ${\displaystyle {\frac {2(1+k)}{k-3}}\,{\sqrt {\frac {k-2}{k}}}\!}$，${\displaystyle k>3}$ ${\displaystyle {\frac {6(k^{3}+k^{2}-6k-2)}{k(k-3)(k-4)}}\!}$，${\displaystyle k>4}$ ${\displaystyle \ln \left({\frac {k}{x_{\mathrm {m} }}}\right)-{\frac {1}{k}}-1\!}$ 未定义 ${\displaystyle k(-ix_{\mathrm {m} }t)^{k}\Gamma (-k,-ix_{\mathrm {m} }t)\,}$

${\displaystyle {\rm {P}}(X>x)=\left({\frac {x}{x_{\min }}}\right)^{-k}}$

${\displaystyle p(x)=\left\{{\begin{matrix}0,&{\mbox{if }}xx_{\min }.\end{matrix}}\right.}$