Some Results on the Generalized Gaussian Distribution

The paper considers information-theoretic applications of a broad class of distributions termed generalized Gaussian (GG). The flexible parametric form of the probability density function of the GG family makes it an excellent choice for many modeling scenarios. Well-known examples of this distribution include Laplace, Gaussian, and uniform. The first part of the paper considers a rate-distortion problem of GG sources under the Lp error distortion. For example, conditions are derived under which Shannon’s lower bound is tight. The second part of the paper develops necessary mathematical properties of the GG distribution needed for the solution of the rate-distortion problem. In particular, it is shown that a GG random variable can be decomposed into a product of a Gaussian random variable and an independent positive random variable. The properties of this decomposition are carefully examined.