Robust estimation for multivariate wrapped models

A weighted likelihood technique for robust estimation of multivariate Wrapped distributions of data points scattered on a $$p-$$ p - dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise inference for standard techniques such as maximum likelihood method. Therefore, there is the need to handle such model inadequacies in the fitting process by a robust technique and an effective downweighting of observations not following the assumed model. Furthermore, the employ of a robust method could help in situations of hidden and unexpected substructures in the data. Here, it is suggested to build a set of data-dependent weights based on the Pearson residuals and solve the corresponding weighted likelihood estimating equations. In particular, robust estimation is carried out by using a Classification EM algorithm whose M-step is enhanced by the computation of weights based on current parameters’ values. The finite sample behavior of the proposed method has been investigated by a Monte Carlo numerical study and real data examples.

Wrapped Zero-inflated Poisson Distribution and Its Properties

Recently, there has been a growing interest in discrete valued wrapped distributions and the trigonometric moments.<br />Characteristic functions of stable processes have been used to study the estimation of the model parameters using<br />estimating function approach (Thavaneswaran et al., 2013). In this paper, we introduce a new discrete circular distribution,<br />the wrapped zero-inflated Poisson distribution and derive its population characteristics.<br /><br />

PARAMETRIC AND NON-PARAMETRIC METHODS FOR THE STUDY OF THE VARIABILITY OF WAVE DIRECTIONS: APPLICATION TO THE ATLANTIC URUGUAYAN COASTS

Wave direction is a fundamental variable in coastal engineering, whether one is interested in analyzing coastal processes or designing harbor structures. In this work a mixture of circular (wrapped) distributions is introduced for modeling the non-stationary probability distribution function of mean wave directions. The proposed distribution is able to accommodate seasonal and inter-annual variability, as well the influence of several climatic indices. This function was applied to the Atlantic Uruguayan coast, finding that both the Tropical South Atlantic index and the Antarctic Oscillation index have a significant influence on the variability of the wave directions.