Approximated fast estimator for the shape parameter of generalized Gaussian distribution

Abstract

Generalized Gaussian distribution (GGD) is often used to characterize the statistical behaviour of a multimedia signal [J.R. Ohm, Multimedia Communication Technology, Representation, Transmission and Identification of Multimedia Signals. Springer, Berlin, 2004]. Although, the estimation of the shape parameter can be based on the maximum likelihood method, this method is computationally demanding. The computational complexity can be reduced by the application of the moment method for the first and second absolute moments. However, this method does not result in small error for the small values of GGD shape parameter. Furthermore, the inversion function often requires storing all control points of a curve. The method presented in this paper approximates the estimation of GGD shape parameter in the range 0.3–3 keeping small relative mean square error (RMSE) for this range. The method is based on the approximation of the moment method in four intervals. The assumed model allows a fast estimation of GGD shape parameter for real-time applications and requires storing only 12 coefficients.