ON CHARACTERIZING DISTRIBUTIONS VIA LINEARITY OF REGRESSION FOR ORDER STATISTICS |
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| Authors: | Jacek Wesolowski Mohammad Ahsanullah |
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| Affiliation: | Mathematical Institute, Warsaw University of Technology, Plac Politechniki 1;, 00–661 Warsaw, Poland. email: Dept of Management Sciences, Rider University, Lawrenceville, NJ 08648-3099;, USA. email: |
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| Abstract: | ![]()
Let X1Xn be a random sample from an absolutely continuous distribution with the corresponding order statistics X1:n≤X2:n≤Xn:n. A complete solution of the problem, posed in 1967 by T. Ferguson, of determining the distribution by linearity of regression of Xk+2:n with respect to Xk:n is given. The only possible distributions are of the exponential, power and Pareto type. A linear regression relation for exponents of order statistics is also considered. |
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| Keywords: | Order statistics linearity of regression exponential distribution power distribution Pareto distribution |
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