Abstract
The relation of Bonferroni-type inequalities to combinatorial problems is demonstrated. An urn model in this setting leads to a statistical paradox as well as to an open problem concerning a statistical test of goodness of fit. An extension of Bonferroni-type inequalities to quadratic inequalities is discussed, which are then applied to the analysis of the structure of pairwisely independent events and of exchangeable events.
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References
Galambos, J. (1969). Quadratic inequalities among probabilities, Annals of the University of Budapest, Section Mathematics, 12, 11–16.
Galambos, J. (1977). Bonferroni inequalities, Annals of Probability, 5, 577–581.
Galambos, J. (1995). Advanced Probability Theory, Second edition, New York: Marcel Dekker.
Galambos, J. and Simonelli, I. (1996a). Bonferroni-type Inequalities with Applications, New York: Springer-Verlag.
Galambos, J. and Simonelli, I. (1996b). An extension of the method of polynomials and a new reduction formula for Bonferroni-type inequalities, Statistics & Probability Letters, 28, 147–151.
Johnson, N. L. and Kotz, S. (1977). Urn Models and Their Applications, New York: John Wiley & Sons.
Koch, G. and Spizzichino, F. (Eds.) (1982). Exchangeability in Probability and Statistics, Amsterdam: North-Holland.
Kolchin, V. F., Sevast’yanov, B. A. and Chistyakov, V. P. (1978). Random Allocations, New York: John Wiley & Sons.
Stoyanov, J. M. (1987). Counterexamples in Probability, New York: John Wiley k Sons.
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© 1997 Birkhäuser Boston
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Galambos, J. (1997). Moments, Binomial Moments and Combinatorics. In: Balakrishnan, N. (eds) Advances in Combinatorial Methods and Applications to Probability and Statistics. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4140-9_16
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DOI: https://doi.org/10.1007/978-1-4612-4140-9_16
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8671-4
Online ISBN: 978-1-4612-4140-9
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