Copulas for statistical signal processing (Part I): Extensions and generalization
Extensions and generalization of copulas families are proposed for exponential, Rayleigh, Weibull, log-normal, Nakagami-m and Rician distributions. To explore the dependence between these distributions, their associated bivariate copula functions are derived from their bivariate probability distributions. To prove the copula functions of bivariate exponential, Rayleigh and Weibull distributions are equivalent and defined using one parameter. To prove log-normal copula is equivalent to the Gaussian one; also simplify the Rician copula function with two parameters. Associated copula density functions are derived; the work fills many blank areas in this field (see in Table 1).
copulas statistical signal processing parameter estimation arbitrary marginal distributions