Journal of Prime Research in Mathematics
Vol. 1 (2006), Issue 1, pp. 217 – 230
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
Probability of the moderate deviations for the sum-functions of spacing
Sherzod Mira
GIK Institute of Engineering Sciences and Technology, Topi-23460, N.W.F.P., Pakistan.
Zam Mirakhmedov
GIK Institute of Engineering Sciences and Technology, Topi-23460, N.W.F.P., Pakistan.
Syed Ikram Abbas Tirmizi
GIK Institute of Engineering Sciences and Technology, Topi-23460, N.W.F.P., Pakistan
\(^{1}\)Corresponding Author: shmirakhmedov@yahoo.com,
Copyright © 2006 Sherzod Mira, Zam Mirakhmedov, Syed Ikram Abbas Tirmizi. 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.
Published: December, 2006.
Abstract
Let \(0=U_{0,n}\leq U_{1,n}\leq … \leq U_{n,n}=1\) be an ordered sample from uniform [0,1] distribution \(D_{in}=U_{i,n}-U_{i-1,n}\), \(i=1,2,..,n\), \(n=1,2,…\) , be their spacings,and let \(f_{1n},…,f_{nn}\) be a set of measurable functions. In this paper theorems on the probabilities of deviations in the moderate zones for \(R_{n}D=f_{1n}(nD_{1n}, … , f_{nn}(nD_{nn}\) are presented. Application of these results to study an intermediate efficiencies of the tests based on statistic \(R_{n}(D)\) are also considered.
Keywords:
Spacings, uniform distribution, large deviations,goodness-offit,asymptotic efficiencies