Probability of the moderate deviations for the sum-functions of spacing

Authors

  • 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.

Keywords:

Spacings, uniform distribution, large deviations, goodness-offit, asymptotic efficiencies

Abstract

Let 0=U0,n≤U1,n≤…≤Un,n=10=U0,n≤U1,n≤…≤Un,n=1 be an ordered sample from uniform [0,1] distribution Din=Ui,n−Ui−1,nDin=Ui,n−Ui−1,n, i=1,2,..,ni=1,2,..,n, n=1,2,…n=1,2,… , be their spacings,and let f1n,…,fnnf1n,…,fnn be a set of measurable functions. In this paper theorems on the probabilities of deviations in the moderate zones for RnD=f1n(nD1n,…,fnn(nDnnRnD=f1n(nD1n,…,fnn(nDnn are presented. Application of these results to study an intermediate efficiencies of the tests based on statistic Rn(D)Rn(D) are also considered.

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Published

2006-12-31

Issue

Vol. 2 No. 1 (2006): Journal of Prime Research in Mathematics

Section

Regular

How to Cite

Probability of the moderate deviations for the sum-functions of spacing. (2006). Journal of Prime Research in Mathematics, 2(1), 217 – 230. https://jprm.sms.edu.pk/index.php/jprm/article/view/27