Quantile function

See also Wikipedia [1229].

Calculating the quantile function from the cdf

ctx.qtf_from cdf(x, cf)

where ctx is dec, mpm, or gmp.

This requires a starting point for a Newton iteration. If a specific starting point is not available, then a Cornish-Fisher expansion can be tried first.

Approximating the quantile function from the cumulant generating function

See inverse Jension saddlepoint approximation for examples

Approximating the quantile function from the cumulants

See Cornish-Fisher expansion for example.