Certain Characterizations of Normal Distribution via Transformations

It is well-known that i.i.d. (independent and identically distributed) normal random variables are transformed into i.i.d. normal random variables by any orthogonal transformation. Less well-known are nonlinear transformations with the above mentioned property, see [2]. In this work we present nonlinear transformations preserving normality, which are more general than the existing ones in the literature.