A Transformation Characterizing the Normal Distribution

In this article we propose a new transformation of random variables (RVs) which characterizes the normal distribution. It allows us to transform n i.i.d. normal RVs whose mean and variance are unknown into new n − 2 i.i.d. new normal variables with zero mean while maintaining the same unknown variance. This belongs to the class of transformations designed to reduce the number of unknown parameters or remove them altogether. Some historical remarks concerning methods for removing parameters in the normal distribution are given and two possible applications of the new transformation are described.