# Benktander Gibrat distribution

Parameters Probability density function No image available Cumulative distribution function No image available $a>0$ (real) $b>0$ (real $x>1$ $e^{-b {\mathrm{Log}[x]}^2}x^{-2-a} \left( -\tfrac{2b}{a} + \left(1 + a + 2b \mathrm{Log}[x]\right)\left(1+\tfrac{2b \mathrm{Log}[x]}{a}\right)\right)$ $1 - e^{-b {\mathrm{Log}[x]}^2} x^{-1-a} \left(1+\tfrac{2b \mathrm{Log}[x]}{a}\right)$ $1+\tfrac{1}{a}$ $\frac{-\sqrt{b}+a e^{\tfrac{(-1+a)^2}{4b}} \sqrt{\pi} \operatorname{erfc}\left(\tfrac{-1+a}{2\sqrt{b}}\right) }{a^2\sqrt{b}}$
$\lim_{b \to 0} \mathrm{Benktander}(a,b) \sim \mathrm{Pareto}(1,a+1) .$