Discordancy tests for two-parameter exponential samples
The inside-out sequential procedures for testing up to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>k</mi> </math> </EquationSource> </InlineEquation> upper outliers in a two-parameter exponential sample are investigated. Six test statistics, one based on the ratio of the difference of largest observation and the sample mean which are unsuspected to be outliers to the range of these observations, and others used for block test procedures discussed in Basu (J Am Stat Assoc 60:548–559, <CitationRef CitationID="CR4">1965</CitationRef>), Balasooriya and Gadag (J Stat Comput Simul 50:249–259, <CitationRef CitationID="CR2">1994</CitationRef>), Zerbet and Nikulin (Commun Stat Theory Methods 32:573–583, <CitationRef CitationID="CR23">2003</CitationRef>) and Kumar (Testing for suspected observations in an exponential sample with unknown origin, <CitationRef CitationID="CR16">2013</CitationRef>), are considered. Utilizing the recursion of Huffer (J Appl Probab 25:346–354, <CitationRef CitationID="CR11">1988</CitationRef>) and algorithm of Lin and Balakrishnan (Comput Stat Data Anal 53:3281–3290, <CitationRef CitationID="CR18">2009</CitationRef>), the critical values of the joint null distributions of these test statistics for sequential testing discordancy of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>k</mi> </math> </EquationSource> </InlineEquation> upper outliers in two-parameter exponential samples on the important cases <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$k= 2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </math> </EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$3$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>3</mn> </mrow> </math> </EquationSource> </InlineEquation> are obtained. We also propose a simple procedure to determine <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>k</mi> </math> </EquationSource> </InlineEquation>, which can reduce the masking or swamping effect. Powers of tests based on these statistics are compared through a Monte Carlo study. Copyright Springer-Verlag Berlin Heidelberg 2015