Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions
Khadiga Arwini; Christopher Dodson
Open Mathematics (2007)
- Volume: 5, Issue: 1, page 50-83
- ISSN: 2391-5455
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] S.-I. Amari, O.E. Barndorff-Neilsen, R.E. Kass, S.L. Lauritzen and C.R. Rao: Differential Geometrical Methods in Statistics, Springer Lecture Notes in Statistics 28, Springer-Verlag, Berlin, 1985.
- [2] S-I. Amari and H. Nagaoka: Methods of Information Geometry, American Mathematical Society, Oxford University Press, 2000.
- [3] Khadiga Arwini: Differential geometry in neighbourhoods of randomness and independence, PhD thesis, UMIST, 2004.
- [4] Khadiga Arwini and C.T.J. Dodson: “Information geometric neighbourhoods of randomness and geometry of the McKay bivariate gamma 3-manifold”, Sankhya: Indian Journal of Statistics, Vol. 66(2), (2004), pp. 211–231. Zbl1192.60008
- [5] Khadiga Arwini and C.T.J. Dodson: “Neighbourhoods of independence for random processes via information geometry”, Math. J., Vol. 9(4), (2005). Zbl1192.60008
- [6] Khadiga Arwini, L. Del Riego and C.T.J. Dodson: “Universal connection and curvature for statistical manifold geometry”, Houston J. Math., in press, (2006). Zbl1126.53021
- [7] Y. Cai, C.T.J. Dodson, O. Wolkenhauer and A.J. Doig: “Gamma Distribution Analysis of Protein Sequences shows that Amino Acids Self Cluster”, J. Theoretical Biology, Vol. 218(4), (2002), pp. 409–418.
- [8] C.T.J. Dodson: “Spatial statistics and information geometry for parametric statistical models of galaxy clustering”, Int. J. Theor. Phys., Vol. 38(10), (1999), pp. 2585–2597. http://dx.doi.org/10.1023/A:1026609310371
- [9] C.T.J. Dodson: “Geometry for stochastically inhomogeneous spacetimes”, Nonlinear Analysis, Vol. 47, (2001), pp. 2951–2958. http://dx.doi.org/10.1016/S0362-546X(01)00416-3 Zbl1042.85500
- [10] C.T.J. Dodson and Hiroshi Matsuzoe: “An affine embedding of the gamma manifold”, Appl. Sci., Vol. 5(1), (2003), pp. 1–6. Zbl1016.60010
- [11] R.J. Freund: “A bivariate extension of the exponential distribution”, J. Am. Stat. Assoc., Vol. 56, (1961), pp. 971–977. http://dx.doi.org/10.2307/2282007 Zbl0106.13304
- [12] T.P. Hutchinson and C.D. Lai: Continuous Multivariate Distributions, Emphasising Applications, Rumsby Scientific Publishing, Adelaide 1990. Zbl1170.62330
- [13] S. Kotz, N. Balakrishnan and N. Johnson: Continuous Multivariate Distributions, Volume 1, 2nd ed., John Wiley, New York, 2000. Zbl0946.62001
- [14] S. Leurgans, T.W.-Y. Tsai and J. Crowley: “Freund’s bivariate exponential distribution and censoring”, In: R.A. Johnson (Ed.): Survival Analysis, IMS Lecture Notes, Hayward, California, Institute of Mathematical Statistics, 1982.
- [15] A.F.S. Mitchell: “The information matrix, skewness tensor and α-connections for the general multivariate elliptic distribution”, Ann. Ins. Stat. Math., Vol. 41, (1989), pp. 289–304. http://dx.doi.org/10.1007/BF00049397 Zbl0691.62049
- [16] Y. Sato, K. Sugawa and M. Kawaguchi: The geometrical structure of the parameter space of the two-dimensional normal distribution, Division of information engineering, Hokkaido University, Sapporo, Japan, 1977. Zbl0443.53046
- [17] L.T. Skovgaard: “A Riemannian geometry of the multivariate normal model”, Scandinavian J. Stat., Vol. 11, (1984), pp. 211–223. Zbl0579.62033