On Transformations of Random Variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 2, pp. 136-149
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In the paper the relationship between asymptotically normal transformations of random variables and the Cornish-–Fisher expansion is established. This relationship enables asymptotically normal transformations to be constructed by a general method. Some generalizations of Wilson–Hilferty and Bartlett transformations may serve as examples. The percentage points of the $\chi^2$-distribution with n degrees of freedom, $n\geq80$, are given. The last example is devoted to the construction of normal random numbers.