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Some limit theorems for ratios of order statistics from uniform random variables
Shou-Fang Xu1,2, Yu Miao3
1Department of Statistics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China.
Journal of Inequalities and Applications
|December 8, 2017
Summary
This study investigates ratios of order statistics from uniform distributions. Researchers established key limit properties, including the almost sure central limit theorem and large deviation principles.
Area of Science:
- Statistics
- Probability Theory
Background:
- Order statistics are crucial in non-parametric statistics.
- Understanding their limiting behavior is essential for statistical inference.
Purpose of the Study:
- To analyze the properties of order statistics ratios from uniform distributions.
- To establish novel limit theorems for these ratios.
Main Methods:
- Utilizing advanced probability theory techniques.
- Applying methods for analyzing convergence properties of random variables.
Main Results:
- Established the almost sure central limit theorem for order statistics ratios.
- Demonstrated the large deviation principle.
- Proved the Marcinkiewicz-Zygmund law of large numbers and complete convergence.
Conclusions:
- The findings provide a deeper understanding of the asymptotic behavior of order statistics ratios.
- These results have implications for statistical modeling and analysis involving uniform distributions.
Keywords:
almost sure central limit theoremcomplete convergencelarge deviation principleorder statisticsuniform distributionMore Related Videos
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