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Three isomorphic vector spaces Bk/N , Ck/N and Dk/N are defined. The interplay of these vector spaces leads to easy proofs for multinomial identities. Using automorphism each multinomial identity is recast into (k + 1)! - 1 more identities. Distributions arising out of some stopping rules in drawing balls of k colors from an urn with and without replacement are connected so that one can easily go from one to the other. Identities involving joint cdf's of order statistics are generalized to those coming from arbitrary multivariate distributions. Discrete distribution similar to multinomial is defined, where all the calculations can be done on usual multinomial distribution and transferred to the general.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Authors:||Balasubramanian, K. and Beg, M.I.|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 11/04|
|Corporate Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||Isomorphic vector space; Urn model; Multinomial identity; Order statistics|
|Deposited By:||DIANE MICHAUD|
|Deposited On:||02 Jun 2010 12:24|
|Last Modified:||08 Dec 2010 18:24|
K. Balasubramanian and M. I. Beg, Three isomorphic vector spaces - applications to binomial identities, urn models and order statististics, Linear Algebra Appl. 388 (2004) 79-89.
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