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April, 1981 Approximation of Product Measures with an Application to Order Statistics
R.-D. Reiss
Ann. Probab. 9(2): 335-341 (April, 1981). DOI: 10.1214/aop/1176994477


Firstly, a well-known upper estimate concerning the distance of independent products of probability measures is extended to the case of signed measures. The upper bound depends on the total variation of the signed measures and on the distances of the single components where the distances are measured in the sup-metric. Under certain regularity conditions, the upper estimate can be sharpened by using asymptotic expansions. These expansions hold true over the set of all integrable function. An application of these results together with an asymptotic expansion of the distribution of a single order statistic yields an asymptotic expansion of the joint distribution of order statistics under the exponential distribution.


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R.-D. Reiss. "Approximation of Product Measures with an Application to Order Statistics." Ann. Probab. 9 (2) 335 - 341, April, 1981.


Published: April, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0462.60037
MathSciNet: MR606998
Digital Object Identifier: 10.1214/aop/1176994477

Primary: 60F99
Secondary: 62E15, 62G30

Rights: Copyright © 1981 Institute of Mathematical Statistics


Vol.9 • No. 2 • April, 1981
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