On the construction of classes of variance stabilizing transformations

Based on the work of Curtiss (1943), Bar-Lev and Enis (1988) presented a proposition providing easily verifiable conditions under which a variance stabilizing and normalizing transformation can be obtained. Here, a proof of that proposition is given, along with a more detailed discussion of this problem. In addition, several examples illustrating the ease of applicability of these conditions are provided and a number of classes of variance stabilizing transformations are presented.