A note on successive comparisons between several ordered variances

ABSTRACT

In this article, a procedure for comparisons between k  (k ⩾ 3) successive populations with respect to the variance is proposed when it is reasonable to assume that variances satisfy simple ordering. Critical constants required for the implementation of the proposed procedure are computed numerically and selected values of the computed critical constants are tabulated. The proposed procedure for normal distribution is extended for making comparisons between successive exponential populations with respect to scale parameter. A comparison between the proposed procedure and its existing competitor procedures is carried out, using Monte Carlo simulation. Finally, a numerical example is given to illustrate the proposed procedure.

KEYWORDS:

• Simultaneous confidence intervals
• Critical constants
• Simulation study
• Recursive integration
• Simple ordering
• Power comparison.

Mathematics Subject Classification:

• 62F30; 62J15

Acknowledgments

The author gratefully acknowledges the helpful suggestions of the referees and the associate editor, which led to appreciable improvements in the quality of paper.

Funding

The author would like to thank the University Grants Commission, Government of India, for financial assistance (F. No. 34-147/2008 (SR)).