2021 / June Volume 16 No.2
Unusual limit theorems for the difference of order statistics from a Pareto
| Published Date |
2021 / June
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|---|---|
| Title | Unusual limit theorems for the difference of order statistics from a Pareto |
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| Download | |
| Pagination | 177-192 |
| Abstract | In this paper we establish various limit theorems for the difference in order statistics from a sample from the Pareto distribution. The underlying density is $f(x)=x^{-2}I(x\ge 1)$. We look at both fixed and slowly increasing samples sizes. For our strong and weak laws of large numbers the first moment will be infinite and for our central limit theorem the second moment will be infinite. These theorems are quite unusual since the usual moment conditions do not hold. In order to achieve these results we must attach weights to these random variables and find these appropriate weights and norming sequences in order to establish our results.
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| DOI | |
| AMS Subject Classification |
60F05, 60F15.
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| Received |
2021-03-21
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| Accepted |
2021-06-27
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