Generalized pearson distributions and related characterization problems

Annals of the Institute of Statistical Mathematics

Volumn 54, Issue 4, 2002, Pages 731-742

  Lefèvre, Claude ^a   Papathanasiou, Vasilis ^b   Utev, Sergey ^c  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF ATHENS   (Greece)

^c UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Characterizations; Covariance identity; Generalized Pearson family of curves; Orthogonal polynomials; Rodrigues' formula

Indexed keywords

FUNCTIONS; POLYNOMIALS; PROBABILITY; PROBLEM SOLVING;

PEARSON CURVES;

RANDOM PROCESSES;

EID: 12244291299     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022403132741     Document Type: Article

References (13)

1. Beale, F. S. (1941). On a certain class of orthogonal polynomials, Ann. Math. Statist., 12, 97-103.
2. Borovkov, A. A. and Utev, S. A. (1983). On an inequality and a related characterization of the normal distribution, Theory Probab. Appl., 28, 209-218.
3. Brascamp, H. J. and Lieb, E. H. (1976). On extensions of the Brunn-Minkowski and Prekopa-Leindner theorems including inequalities for the log concave functions and with applications to the diffusion equation, J. Funct. Anal., 22, 366-389.
4. Cacoullos, T. and Papathanasiou, V. (1989). Characterizations of distributions by variance bounds, Statist. Probab. Lett, 7, 351-356.
5. Cacoullos, T. and Papathanasiou, V. (1995). A generalization of covariance identity and related characterizations, Math. Methods Statist., 4, 106-113.
6. Cacoullos, T., Papathanasiou, V. and Utev, S. A. (1994). Variational inequalities with examples and an application to the central limit theorem, Ann. Probab., 22, 1607-1618.
7. Diaconis, P. and Zabell, S. (1991). Closed form summation for classical distributions: Variations on a theme of De Moivre, Statist. Sci., 6, 284-302.
8. Dunning, K. A. and Hanson, J. N. (1977). Generalized Pearson distributions and nonlinear programming, J. Statist. Comput. Simulation, 6, 115-128.
9. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, Vol. 1, 2nd ed., Wiley, New York.
10. Korwar, R. M. (1991). On characterizations of distributions by mean absolute deviation and variance bounds, Ann. Inst. Statist. Math., 43, 287-295.
11. Ord, J. K. (1972). Families of Frequency Distributions, Charles Griffin, London.
12. Papathanasiou, V. (1995). A characterization of the Pearson system of distributions and the associated orthogonal polynomials, Ann. Inst. Statist. Math., 47, 171-176.
13. Utev, S. A. (1989). Probability problems connected with a certain integrodifferential inequality, Siberian Math. J., 30, 490-493.