Let x be a random variable with a density function f(x) with a mean of zero and a variance of 1. Let β1 be the skewness of this distribution and let β2 be its kurtosis. Let z be a normally distributed random variable and let zα be the value of z at the αth percentile.
As an illustration of this last definition when α = 0.95, zα = 1.96
where ωα is the corresponding value for f(x).
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- Fisher RA and Cornish EA (1960) The percentile points of distributions having known cumulants. Technometrics 2: 209–225
- Abramowitz M and Stegun I (1965) Handbook of mathematical functions, with formulas, graphs and mathematical tables. Dover Publications, New York