Linearity of regression for adjacent order statistics-discrete case

• Autorzy: Dembińska A.
• Języki publikacji: EN

Abstrakty

EN

Let X1X2 be a random sample from a discrete distribution on the integers with the corresponding order statistics X1:2<X2:2. In [5] Nagaraja considered the 1problem of characterizing distributions with the property E(Xi:2]Xj:2,X2:2 - X1:2> m) = ajXj:2+bj where m is a nonnegative integer, a, b -some constants and i,j należy {1,2}, i = j. However some of the main results of that paper are not complete or incorrect. In this note, developing Nagaraja's ideas, the family of distributions with the linearity of regression property is completely characterized.

Słowa kluczowe

EN

order statistics; geometric distribution; linearity of regression

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 3
• Strony: 711--721
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Dembińska A.

• Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warsaw, Poland

Bibliografia

• [1] C. Jordan, Calculus of Finite Differences, Third Edition. Chelsea, New York (1965).
• [2] S. N. U. A. Kirmani, S. N. Alam, Characterization of the geometric distribution by the form of a predictor, Comm. Statist.-Theory Methods A 9(5) (1980), 541-547.
• [3] G. Letac, V. Seshadri, A characterization of the generalized inverse Gaussian distribution by vontinued fractions, Z. Wahrsch. verw. Gebiete 62 (1983), 485-489.
• [4] F. López-Blázquez, B. Salamanca Miño, A characterization of the geometric distribution, Statist. Papers 39 (1998), 231-236.
• [5] H. N. Nagaraja, Some characterizations of discrete distributions based on linear regressions of adjacent order statistics, J. Statist. Plann. Inference 20 (1988), 65-75.
• [6] C. D. Olds, Continued Fractions, Vol 9. New Mathematical Library. Random House 1963.
• [7] I. M. Rhyzhik, I. S. Gradshteyn, Tables of Integrals, Sums, Series and Products, Gosud. Izd. Tech.-Teoretich. Lit., Moscow (1951) (in Russian).