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October, 1972 Convergence of Quantile and Spacings Processes with Applications
Galen R. Shorack
Ann. Math. Statist. 43(5): 1400-1411 (October, 1972). DOI: 10.1214/aoms/1177692373


The quantile process was shown by Bickel to converge in the uniform metric on intervals $\lbrack a, b\rbrack$ with $0 < a < b < 1$. By introducing appropriate new supremum metrics, this result is extended to all of (0, 1). Hence a natural process of ordered spacings from the uniform distribution converges in certain supremum metrics. This is used to establish the limiting normality of a large family of statistics based on ordered spacings, which can be used in testing for exponentiality. The non-null case is also considered.


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Galen R. Shorack. "Convergence of Quantile and Spacings Processes with Applications." Ann. Math. Statist. 43 (5) 1400 - 1411, October, 1972.


Published: October, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0249.62021
MathSciNet: MR359133
Digital Object Identifier: 10.1214/aoms/1177692373

Rights: Copyright © 1972 Institute of Mathematical Statistics


Vol.43 • No. 5 • October, 1972
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