The $ k $-th smallest spacing $ m_{n}(k) $ induced by $ n $ uniformly distributed order statistics on $ (0, 1) $ was considered in this paper. It has been known that $ n^2m_{n}(k) $ possesses a limiting distribution as $ n $ tends to infinity. In this paper (large) deviation probabilities of $ n^2m_{n}(k) $ to zero or infinity are studied, with $ k $ possibly depending on $ n. $ This study generalized a result obtained by Devroye in their 1982 paper.
Citation: Mainza Mbokoma. Large deviations of small uniform spacings[J]. AIMS Mathematics, 2026, 11(8): 24978-24986. doi: 10.3934/math.20261004
The $ k $-th smallest spacing $ m_{n}(k) $ induced by $ n $ uniformly distributed order statistics on $ (0, 1) $ was considered in this paper. It has been known that $ n^2m_{n}(k) $ possesses a limiting distribution as $ n $ tends to infinity. In this paper (large) deviation probabilities of $ n^2m_{n}(k) $ to zero or infinity are studied, with $ k $ possibly depending on $ n. $ This study generalized a result obtained by Devroye in their 1982 paper.
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Mainza Mbokoma. Large deviations of small uniform spacings[J]. AIMS Mathematics, 2026, 11(8): 24978-24986. doi: 10.3934/math.20261004
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