Log-logistic distribution
= Log-logistic distribution
{title2=$F(x)=\frac{(x/a)^\kappa}{1+(x/a)^\kappa}$}
For scale $a>0$ and shape $\kappa>0$, the log-logistic distribution has the displayed cumulative distribution function for $x\geq0$, with density $(\kappa/a)(x/a)^{\kappa-1}/[1+(x/a)^\kappa]^2$ for $x>0$. Its log-odds are affine in $\log x$, giving the name and motivating a <log-logistic probability plot>. In the exam's parameterization, $a=\alpha$ and $\kappa=\beta-1$.