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Exact Laws for Sums of Order Statistics from a Generalized Pareto Distribution |
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| Abstract: | Abstract We select the kth order statistic from each row from a sequence of independent and identically distributed random variables from a distribution that generalizes the Pareto distribution. We then examine weighted sums of these order statistics to see whether or not Laws of Large Numbers with nonzero limits exist. |
| Keywords: | Almost sure convergence Weak law of large numbers Strong law of large numbers Exact laws Slow variation |