I'm Xavier Vigan, a physical oceanographer.
I've been using your $f(x)=\dfrac 12 \times \left(X+C-\sqrt{S+(X-C)^2}\right)$ function to calibrate quantile vs quantile plots.
Because of the shape of the tail of my distribution towards $+\infty$, do you know how I could modify your function such that it's asymptote towards $+\infty$ is $Y=A\times x$ instead of $Y=A$ ?
Many thanks for your help!
Best regards,
Xavier