Simultaneous testing for the successive differences of exponential location parameters under heteroscedasticity

Simultaneous confidence intervals for ordered pairwise differences of exponential location parameters under heteroscedasticity

“…The proof of Theorem 2.1 is on similar lines to the proof of Theorem 1 given in Maurya et al (2011).…”

“…Let F −1 2,2m−2 (1 − α) be the 100(1 − α)th percentile and F 2,2m−2 (x) be the value of the cumulative distribution function at x of the F distribution with (2, 2m − 2) d.f. The following theorem shows that the critical constants, for the given values of k, m and α, used in Maurya et al (2011) for confidence intervals for the class of successive differences can also be used for confidence intervals for larger classes of ordered pairwise differences.…”

“…Recently, using Lam's (1987Lam's ( , 1988 technique, Maurya et al (2011) proposed two-stage and one-stage procedures for successive comparisons under heteroscedasticity. In this article, simultaneous confidence intervals of ordered pairwise differences are proposed and it is proved that the critical constants for confidence intervals for the class of successive differences under heteroscedasticity used by Maurya et al (2011) can also be used for confidence intervals for the larger classes of ordered pairwise differences proposed in this article. Hence, one will have the same confidence intervals for the differences between successive location parameters.…”

“…For when an additional sample is not available, a onestage multiple-comparison procedure is proposed, in Section 3, for ordered pairwise differences of location parameters. In Section 4, power comparison, using Monte Carlo simulation, of the proposed procedures with the procedures proposed by Maurya et al (2011) is discussed.…”

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a b s t r a c tThis article deals with the extension of the two-stage and one-stage procedures for successive differences of location parameters of k independent two-parameter exponential distributions proposed by Maurya et al (2011). While maintaining the advantages of the Maurya et al (2011) procedure, our proposed procedure has more power for rejecting the null hypothesis of homogeneity of several location parameters in favour of the alternative.

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