2020 / March Volume 15 No.1
Exact Strong Laws for the Range
| Published Date |
2020 / March
|
|---|---|
| Title | Exact Strong Laws for the Range |
| Author | |
| Keyword | |
| Download | |
| Pagination | 53-63 |
| Abstract | In this paper we establish exact strong laws of large numbers for the range of a Pareto random variable. The underlying density is $f(x)=x^{-2}I(x\ge 1)$. Neither the first nor second moments of this random variable
exist, which makes these theorems unusual. The
results are of the form $\sum_{i=1}^n a_i R_i/b_n\to \gamma,$ as $n \to\infty$, where $R_i$ is the range from the $i^{th}$ sample.
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| DOI | |
| AMS Subject Classification |
60F15
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| Received |
2019-12-14
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