On Transformations of Random Variables

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.