Geometrical properties of Pareto distribution
作者： N.H. Abdel-All , M.A.W. Mahmoud , H.N. Abd-Ellah
DOI: 10.1016/S0096-3003(02)00490-3
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摘要: The differential-geometrical framework for analyzing statistical problems related to Pareto distribution, is given. A classical and intuitive way of description the relationship between differential geometry statistics, introduced [Publicationes Mathematicae Debrecen, Hungary, vol. 61 (2002) 1-14; RAAG Mem. 4 (1968) 373; Ann. Statist. 10 (2) (1982) 357; Springer Lecture Notes in Statistics, 1985; Tensor, N.S. 57 (1996) 282; Commun. Theor. Meth. 29 (4) (2000) 859; 33 (1979) 347; Int. J. Eng. Sci. 19 (1981) 1609; 300; Differential Geometry 1993], but a slightly modified manner. This order provide an easier introduction readers not familiar with geometry. parameter space distribution using its Fisher's matrix defined. Riemannian scalar curvatures are calculated. equations geodesics obtained solved. J-divergence, geodesic distance relations them that found. development relation J-divergence illustrated. curvature J-space represented.
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sci-hub.se 参考文章(23)
C. Radhakrishna Rao, Information and the Accuracy Attainable in the Estimation of Statistical Parameters Bull Calcutta. Math. Soc.. ,vol. 37, pp. 235- 247 ,(1992) , 10.1007/978-1-4612-0919-5_16
Shun-ichi Amari, Differential-geometrical methods in statistics ,(1985)
Arthur Cecil Pigou, The Economics of Welfare ,(1920)
Anwar M. Hossain, William J. Zimmer, Comparisons of methods of estimation for a Pareto distribution of the first kind Communications in Statistics-theory and Methods. ,vol. 29, pp. 859- 878 ,(2000) , 10.1080/03610920008832520
A.A. Abdel-Ghaly, A.F. Attia, H.M. Aly, Estimation of the parameters of pareto distribution and the reliability function usin accelerated life testing with censoring Communications in Statistics - Simulation and Computation. ,vol. 27, pp. 469- 484 ,(1998) , 10.1080/03610919808813490
Barry C. Arnold, S.James Press, Bayesian inference for pareto populations Journal of Econometrics. ,vol. 21, pp. 287- 306 ,(1983) , 10.1016/0304-4076(83)90047-7
Yoshiharu Sato, Kazuaki Sugawa, Michiaki Kawaguchi, The geometrical structure of the parameter space of the two-dimensional normal distribution Reports on Mathematical Physics. ,vol. 16, pp. 111- 119 ,(1979) , 10.1016/0034-4877(79)90043-0
Shun-Ichi Amari, Differential Geometry of Curved Exponential Families-Curvatures and Information Loss Annals of Statistics. ,vol. 10, pp. 357- 385 ,(1982) , 10.1214/AOS/1176345779
Barry C. Arnold, S. James Press, Bayesian Estimation and Prediction for Pareto Data Journal of the American Statistical Association. ,vol. 84, pp. 1079- 1084 ,(1989) , 10.1080/01621459.1989.10478875
John W. Rice, Michael K. Murray, Differential Geometry and Statistics ,(1993)