Cornish–Fisher expansion

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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 up and xp , respectively, and let kr be the rth cumulant of the distribution of interest. Then, for all p,.

Subjects: Probability and Statistics.

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