Secant methods with transformations: A faster and more robust approach to computing quantiles (Q1965933)

Let \(F\) be a continuous distribution function, \(0<p<1\). To find the quantile \(q\) of the level \(p\) for \(F\) (i.e. to solve \(F(q)=p\)) it is proposed to solve the equation \( \log({F(x)\over 1-F(x)}) =\log({p\over 1-p}) \) iteratively by the secant method. If the domain of \(F\) is \([0,+\infty)\) or \([0,1]\) an additional transformation of the domain into \((-\infty,+\infty)\) is proposed. The applications of this method to the calculation of the non-central \(t\)-distribution and non-central \(\chi^2\)-distribution quantiles are considered.