Physics Commons^™

Multi-Gaussian Random Variables For Modeling Optical Phenomena, Olga Korotkova, Milo W. Hyde Iv

Faculty Publications

A generalization of the classic Gaussian random variable to the family of multi-Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability density function (PDF) of the MG family members is an alternating series of Gaussian functions with suitably chosen heights and widths. In particular, for integer values of M, the series has a finite number of terms and leads to flattened profiles, while reducing to the classic Gaussian PDF for M = 1. For non-integer, positive values of M, a convergent infinite series of …