Limit Theorems for Randomly Selected Ratios of Order Statistics from a Pareto Distribution |
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| Authors: | André Adler |
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| Institution: | 1. Department of Mathematics , Illinois Institute of Technology , Chicago, Illinois, USA adler@iit.edu |
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| Abstract: | Abstract Consider independent and identically distributed random variables {X nk , 1 ≤ k ≤ m, n ≥ 1} from the Pareto distribution. We randomly select a pair of order statistics from each row, X n(i) and X n(j), where 1 ≤ i < j ≤ m. Then we test to see whether or not Strong and Weak Laws of Large Numbers with nonzero limits for weighted sums of the random variables X n(j)/X n(i) exist where we place a prior distribution on the selection of each of these possible pairs of order statistics. |
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| Keywords: | Almost sure convergence Exact laws Order statistics Strong law of large numbers Weak law of large numbers |
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