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


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© Wolf-Dieter Richter; Licensee Bentham Open.

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/legalcode), which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* 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.