The Open Mathematics, Statistics and Probability Journal

2016, 7 : 1-9
Published online 2016 April 20. DOI: 10.2174/1876527001607010001
Publisher ID: TOSPJ-7-1

RESEARCH ARTICLE
 Skewness-Kurtosis Controlled Higher Order Equivalent Decisions

Wolf-Dieter Richter, *
University of Rostock, Institute of Mathematics , Ulmenstraße 69, Haus 3, 18057 Rostock, Germany

* Address correspondence to this author at the University of Rostock, Institute of Mathematics Ulmenstraße 69, Haus 3, 18057 Rostock, Germany; Tel: +493874986663; Fax: +493814986553; E-mail: wolf-dieter.richter@uni-rostock.de

ABSTRACT

We define equivalence of asymptotic Gaussian expectation tests when error probabilities of first kind are approaching zero at the same restricted speed for both tests and if the same holds true for the error probabilities of second type which are measured at a moderate locally chosen alternative. To ensure such equivalence, the influence of skewness and kurtosis parameters is studied.

Keywords:

Adjusted quantiles, adjusted statistics, AMS 2010 Subject Classification 62C05, 62F03, 62E20 (Primary), 60F10 (Secondary), error probabilities, expectation test, large Gaussian quantiles, moderate local alternative, process control.