The SPML model under the general projected normal distribution / Amani Abubakr Mohammed Ahmed ; Supervised Abdelnasser Saad , Moshira Ahmed Ismail , Alyaa Roshdy Zahran

Thesis (Ph.D.) - Cairo University - Faculty of Economics and Political Science - Department of Statistics

The general projected normal distribution (GPND) is a flexible distribution family that is used for modeling circular data. The spherically projected multivariate linear (SPML) model was introduced in the literature for circular linear regression utilizing the GPND assuming identity covariance matrix (V=1). In this study, we are concerned with formulation and estimation of the SPML regression model under the GPND assuming general structure of the covariance matrix. A special case of a location model assumingV=v I, is analyzed where the circular parameters are estimated using maximum likelihood estimation and method of moments. Then, we consider maximum likelihood estimation of the location model assuming the GPND. EMalgorithm and Newton Raphson method are formulated and EM-algorithm has better performance than Newton Raphson method. Finally, the SPML model is formulated and estimated using EMalgorithm.Based on the simulation study, the estimated circular parameters show good behavior for different scenarios. The results show that the behavior of the estimated regression parameters is affected by the structure of V . Also, estimation of V affects the bias of the estimated regression coefficients. However, the estimated regression parameters have consistent behavior

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