Abstract
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, $n \geqq 80$, are given.The last example is devoted to the construction of normal random numbers.
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