Simultaneous one-sided confidence intervals for the ordered pairwise differences of exponential location parameters

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

“…θ 1 = · · · = θ k = θ , Chen (1982) and Dhawan and Gill (1997) discussed test procedures for testing the null hypothesis H 0 : µ 1 = · · · = µ k against the simple ordered alternative H 1 : µ 1 ≤ · · · ≤ µ k with at least one strict inequality, and inverted the test statistic to obtain simultaneous confidence intervals for the differences µ j − µ i , 1 ≤ i < j ≤ k of exponential location parameters. In the literature, Marcus (1976), Hayter (1990) and Hayter and Liu (1996) and references cited therein have addressed the related problems of testing homogeneity against simple ordered alternative; other references cited are Barlow et al (1972), Robertson et al (1988), Hochberg and Tamhane (1987).…”

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

“…, k − 1 (two-sided problem) and discussed the associated simultaneous confidence intervals for (k − 1) differences between successive location parameters under the assumption that unknown scale parameters are equal. The class of differences of location parameters in the Singh et al (2006) procedure was smaller than the class of differences considered by Dhawan and Gill (1997). The critical constants required to derive the simultaneous confidence intervals for successive differences of exponential location parameters using Singh et al (2006) were smaller than those of the Dhawan and Gill (1997) procedure.…”

“…The critical constants required to derive the simultaneous confidence intervals for successive differences of exponential location parameters using Singh et al (2006) were smaller than those of the Dhawan and Gill (1997) procedure. Therefore, in comparison to the Dhawan and Gill (1997) procedure, the Singh et al (2006) procedure has more ability to make decisions of the form µ i+1 − µ i > 0 but has less power for rejecting the null hypothesis of homogeneity against the ordered alternative; see Haibing (2009).…”

“…The assumption of equality of scale parameters is seldom borne out by the experimenter data, which limits the applications of the Dhawan and Gill (1997) and Singh et al (2006) procedures. Recently, using Lam's (1987Lam's ( , 1988 technique, Maurya et al (2011) proposed two-stage and one-stage procedures for successive comparisons under heteroscedasticity.…”

“…For details, we refer the reader to Marcus (1976), Hayter (1990), Lee and Spurrier (1995), Chen (1982), Liu et al (2000) and references cited therein. For the case of unknown and equal scale parameters, Dhawan and Gill (1997) proposed a test procedure for testing the null hypothesis of the homogeneity of k location parameters against the simple ordered alternative, and derived associated simultaneous confidence intervals for…”