A class of distributions connected to order statistics with nonintegral sample size |
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| Authors: | Vijay K. Rohatgi A.K.Md. Ehsanes Saleh |
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| Affiliation: | 1. Bowling Green State University , Bowling Green, Ohio, 43403;2. Carleton University , Ottawa, K15 5B6, Canada |
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| Abstract: | Newton's binomial series expansion is used to develop a (class of) distribution function(s) Fr:∝ which may be interpreted as the distribution of the rthorder statistic with nonintegral sample size∝. It is shown that Fr:∝ has properties similar to Fr:n. Multivariate extension is considered and an elementary proof of the integral representation for the joint distribution of a subset of order statistics is given. An application is included. |
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| Keywords: | order statistics nonintegrai sample size integral representation binomial series combinatorial identity |
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