  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 of the MG family members is the alternating series
of the Gaussian functions with the suitably chosen heights and widths. In
particular, for the integer values of M the series has finite number of terms
and leads to flattened profiles, while reducing to classic Gaussian density for
M = 1. For non-integer, positive values of M a convergent infinite series of
Gaussian functions is obtained that can be truncated in practical problems.
While for all M > 1 the MG PDF has attened profiles, for 0 < M < 1 it leads to
cusped profiles. Moreover, the multivariate extension of the MG random variable
is obtained and the Log-Multi-Gaussian (LMG) random variable is introduced.
