A new alpha and gamma based mixture approximation for heavy-tailed Rayleigh distribution

In this paper, a novel bi-parameter mixture approximation for modeling the statistical properties of heavy-tailed Rayleigh distribution is developed. Heavy-tailed Rayleigh distribution is basically the amplitude PDF of bi-variate isotropic α-stable distribution which appears in the envelope distribution of impulsive interferences and SAR return signals. Closed-form expression for PDF is a serious consideration in signal processing with α-stable distribution. In this case, mixture approximation by means of Rayleigh and a generalization of Cauchy distribution is a simple but comprehensive approach. Several models try to give a model for the mixture ratio based on α. We propose two new methods for mixture ratio estimation based on both α and γ. Numerical results verify that the proposed mixture approximation is closer to the theoretical and empirical heavy-tailed Rayleigh distribution.