On Transformations of Random Variables
L. N. Bol’shev · Theory of Probability and Its Applications · 1959
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.