Department of Actuarial ScienceInstituto Tecnolo´gico Auto´nomo de M´exicoR´io Hondo No. 1, Col. Progreso Tizap´an, C.P. 01080, M´exico D.F., M´exicoe-mail: mercedes@itam.mxAbstract: In Fern´andez-Duran [4], a new family of circular distributionsbased on nonnegative trigonometric sums (NNTS models) is developed.Because the parameter space of this family is the surface of the hypersphere,an efficient Newton-like algorithm on manifolds is generated in order toobtain the maximum likelihood estimates of the parameters.AMS 2000 subject classifications: Primary 49M15, 62G07; secondary49Q99.Keywords and phrases: Differential geometry, maximum likelihood es-timation, Newton algorithm, nonnegative Fourier series, smooth Riemannmanifold.Received November 2010.