Test of Homogeneity Against Umbrella Scale Alternative Based on Sample Spacings

Abstract

In this paper, a test procedure based on sample spacings for testing homogeneity of scale parameters against umbrella ordered alternative with at least one strict inequality is proposed. The exact critical points through simulation are computed for the proposed test in case of standard exponential, standard logistic and standard uniform distributions; however the proposed test can be applied even in case of other distributions like Laplace, Pareto, Weibull, etc. Construction of Simultaneous one-sided confidence intervals (SOCIs) is proposed along with an illustration. Power of the proposed test is computed and some power comparisons are also made.

Keywords:

• Sample Spacings
• Umbrella ordering
• Critical point computation
• Simultaneous one-sided confidence intervals
• Statistical simulation