= Log-logistic probability plot
{title2=$\log\frac{F(x)}{1-F(x)}=(\beta-1)\log x-(\beta-1)\log\alpha$}
For $F(x)=1-[1+(x/\alpha)^{\beta-1}]^{-1}$, plotting the logits of $p_i=i/(n+1)$ against sorted log observations gives an approximately straight line under the model. The <probability integral transform> makes $F(X_{(i)})$ a uniform order statistic with expectation $i/(n+1)$, motivating these plotting positions. With those axes the slope is $\beta-1$ and the intercept is $-(\beta-1)\log\alpha$.
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