Approximate Formulas for the Percentage Points and Normalization of $t$ and $x^2$

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Abstract
The Cornish-Fisher method is used to express Student''s t as a series of terms in decreasing powers of [image], the number of degrees of freedom, each term being a polynomial in x, a standardized normal variate. Any required percentage point of t for any [image] can be obtained approx. by substituting in this series the corresponding percentage point of the normal variate x; a tab e is given to facilitate the arithmetic of this substitution. A similar formula and table are given for x 2. Comparison with true values shows that for 10 or more degrees of freedom the approximations are highly accurate and superior to others in common use. Inverse formulae are also given, that is, polynomials in t and in x 2 whose distr. will be approx. normal.

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