The probability of large deviations for the sum functions of spacings

Mirakhmedov, Sherzod Mira'zam

doi:https://doi.org/10.1155/IJMMS/2006/58738

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 058738 | https://doi.org/10.1155/IJMMS/2006/58738

The probability of large deviations for the sum functions of spacings

Sherzod Mira'zam Mirakhmedov¹

Received16 Mar 2004

Revised23 Nov 2005

Accepted28 Nov 2005

Published12 Apr 2006

Abstract

Let 0=U0,n≤U1,n≤⋯≤Un−1,n≤Un,n=1 be an ordered sample from uniform [0,1] distribution, and Din=Ui,n−Ui−1,n, i=1,2,…,n; n=1,2,…, be their spacings, and let f1n,…,fnn be a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statistics Rn(D)=f1n(nD1n)+⋯+fnn(nDnn) are proved. Application of these theorems for determination of the intermediate efficiencies of the tests based on Rn(D)-type statistic is presented here too.

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Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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