Multivariate Nonnegative Trigonometric Sums Distributions for High-Dimensional Multivariate Cirular Data
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Fernández-Durán and Gregorio-Domínguez (2014) defined a family of probability distributions for a vector of circular random variables by considering multiple nonnegative trigonometric sums. These distributions are highly flexible and can present many modes and skewness. Several operations on these multivariate distributions are translated into operations on the vector of parameters; for example, marginalization involves the calculation of the eigenvectors and eigenvalues of a matrix and, independence among subsets of the elements of the vector of circular variables translates to a case in which the vector of parameters is the Kronecker product of the corresponding subsets of the vector of parameters. An alternative parameter estimation algorithm for high-dimensional circular data is presented and applied to a real dataset on wind directions.
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