I am trying to understand how to derive the quantile function from the cdf. The Singh-Maddala cdf is enter image description here

Should i just solve for x ?

Thank you

  • 2
    $\begingroup$ Yes: that's what "deriving" the quantile function means, doesn't it? $\endgroup$
    – whuber
    Commented Aug 2, 2016 at 23:05
  • $\begingroup$ This may help you see that the answer is "yes". $\endgroup$
    – Glen_b
    Commented Aug 3, 2016 at 10:19

1 Answer 1


In case you were still wondering, solving $F(x)=u$ in $x$ leads to $$ Q(u) = b\Big((1-u)^{-1/q}-1\Big)^{1/a},$$ where $u$ is a realisation of standard uniform variate. To generate Singh-Maddala random variates, $1-u$ can be replaced simply by $u$.


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