Limit theorems for randomly selected adjacent order statistics from a Pareto distribution
Consider independent and identically distributed random variables {Xnk, 1≤k≤m, n≥1} from the Pareto distribution. We randomly select two adjacent order statistics from each row, Xn(i) and Xn(i+1), where 1≤i≤m−1. Then, we test to see whether or not strong and weak laws of large numbers with nonzero...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3427 |
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| _version_ | 1849308110397636608 |
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| author | André Adler |
| author_facet | André Adler |
| author_sort | André Adler |
| collection | DOAJ |
| description | Consider independent and identically distributed random variables
{Xnk, 1≤k≤m, n≥1} from the Pareto distribution. We randomly select two adjacent order statistics from each row, Xn(i) and Xn(i+1), where 1≤i≤m−1. 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
Xn(i+1)/Xn(i) exist, where we place a prior distribution on the selection of each of these possible pairs of order statistics. |
| format | Article |
| id | doaj-art-13d2c50ae7834ea58b98d30b604e69fa |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-13d2c50ae7834ea58b98d30b604e69fa2025-08-20T03:54:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005213427344110.1155/IJMMS.2005.3427Limit theorems for randomly selected adjacent order statistics from a Pareto distributionAndré Adler0Department Applied of Mathematics, College of Science and Letters, Illinois Institute of Technology, Chicago 60616, IL, USAConsider independent and identically distributed random variables {Xnk, 1≤k≤m, n≥1} from the Pareto distribution. We randomly select two adjacent order statistics from each row, Xn(i) and Xn(i+1), where 1≤i≤m−1. 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 Xn(i+1)/Xn(i) exist, where we place a prior distribution on the selection of each of these possible pairs of order statistics.http://dx.doi.org/10.1155/IJMMS.2005.3427 |
| spellingShingle | André Adler Limit theorems for randomly selected adjacent order statistics from a Pareto distribution International Journal of Mathematics and Mathematical Sciences |
| title | Limit theorems for randomly selected adjacent order statistics from a Pareto distribution |
| title_full | Limit theorems for randomly selected adjacent order statistics from a Pareto distribution |
| title_fullStr | Limit theorems for randomly selected adjacent order statistics from a Pareto distribution |
| title_full_unstemmed | Limit theorems for randomly selected adjacent order statistics from a Pareto distribution |
| title_short | Limit theorems for randomly selected adjacent order statistics from a Pareto distribution |
| title_sort | limit theorems for randomly selected adjacent order statistics from a pareto distribution |
| url | http://dx.doi.org/10.1155/IJMMS.2005.3427 |
| work_keys_str_mv | AT andreadler limittheoremsforrandomlyselectedadjacentorderstatisticsfromaparetodistribution |