A form of the Edgeworth expansion, introduced by Cornish and Sir Ronald Fisher in 1937. In its most-used inverse form, it relates the cumulative distribution function of a normal distribution to some distribution of interest.

Denote the 100p percentiles of the normal distribution and of the distribution of interest by u_p and x_p , respectively, and let k_r be the rth cumulant of the distribution of interest. Then, for all p,