Maximum likelihood characterization of rotationally symmetric distributions on the sphere

Aczél, J. and Dhombres, J. (1989). Functional equations in several variables with applications to mathematics, information theory and to the natural and social sciences. In Encyclopedia Math. Appl., vol. 31. Cambridge University Press, Cambridge.

Arnold, K.J. (1941). On spherical probability distributions. Ph.D. thesis, Massachusetts Institute of Technology.

Azzalini, A. and Genton, M.G. (2007). On Gauss’s characterization of the normal distribution. Bernoulli, 13, 169–174.

Bingham, M.S. and Mardia, K.V. (1975). Characterizations and applications. In Statistical Distributions for Scientific Work, vol. 3, (G.P. Patil, S. Kotz and J.K. Ord, eds.). Reidel, Dordrecht and Boston, pp. 387–398.

Breitenberger, E. (1963). Analogues of the normal distribution on the circle and the sphere. Biometrika, 50, 81–88.

Chang, T. (2004). Spatial statistics. Statist. Sci., 19, 624–635.

Duerinckx, M., Ley, C. and Swan, Y. (2012). Maximum likelihood characterization of distributions. arXiv:1207.2805.

Fisher, R.A. (1953). Dispersion on a sphere. Proc. R. Soc. Lond. Ser. A, 217, 295–305.

Fisher, N.I. (1985). Spherical medians. J. R. Stat. Soc. Ser. B, 47, 342–348.

Gauss, C.F. (1809). Theoria motus corporum coelestium in sectionibus conicis solem ambientium. Perthes et Besser, Hamburg. English translation by C.H. Davis, reprinted by Dover, New York (1963).

Jones, M.C. and Pewsey, A. (2005). A family of symmetric distributions on the circle. J. Amer. Statist. Assoc., 100, 1422–1428.

Kagan, A.M., Linnik, Y.V. and Rao, C.R. (1973). Characterization problems in mathematical statistics. Wiley, New York.

Langevin, P. (1905). Sur la théorie du magnétisme. J. Phys., 4, 678–693; Magnétisme et théorie des électrons. Ann. Chim. Phys., 5, 70–127.

Ley, C., Swan, Y., Thiam, B. and Verdebout, T. (2013). Optimal R-estimation of a spherical location. Stat. Sinica, 23, to appear.

Mardia, K.V. (1972). Statistics of directional data. Academic Press, London.

Mardia, K.V. (1975a). Statistics of directional data. J. R. Stat. Soc. Ser. B, 37, 349–393.

Mardia, K.V. (1975b). Characterization of directional distributions. In Statistical Distributions for Scientific Work, vol. 3, (G.P. Patil, S. Kotz and J.K. Ord, eds.). Reidel, Dordrecht and Boston, pp. 365–385.

Mardia, K.V. and Jupp, P.E. (2000). Directional statistics. Wiley, Chichester.

Purkayastha, S. (1991). A rotationally symmetric directional distribution: obtained through maximum likelihood characterization. Sankhyā Ser. A, 53, 70–83.

Saw, J.G. (1978). A family of distributions on the m-sphere and some hypothesis tests. Biometrika, 65, 69–73.

Von Mises, R. (1918). Uber die ‘Ganzzahligkeit’ der Atomgewichte und verwandte Fragen. Phys. Z., 19, 490–500.

Watson, G.S. (1982). Distributions on the circle and sphere. J. Appl. Probab., 19, 265–280.

Watson, G.S. (1983). Statistics on spheres. Wiley, New York.

Whittaker, E.T. and Watson, G.N. (1990). A Course in Modern Analysis, 4th edn. Cambridge University Press.