Approximated non parametric confidence regions for the ratio of two percentiles

ABSTRACT

In the wood industry, it is common practice to compare in terms of the ratio of the same-strength properties for lumber of two different dimensions, grades, or species. Because United States lumber standards are given in terms of population fifth percentile, and strength problems arise from the weaker fifth percentile rather than the stronger mean, so the ratio should be expressed in terms of the fifth percentiles rather than the means of two strength distributions. Percentiles are estimated by order statistics. This paper assumes small samples to derive new non parametric methods such as percentile sign test and percentile Wilcoxon signed rank test, construct confidence intervals with covergage rate 1 – αx for single percentiles, and compute confidence regions for ratio of percentiles based on confidence intervals for single percentiles. Small 1 – αx is enough to obtain good coverage rates of confidence regions most of the time.

KEYWORDS:

• Confidence region
• Percentile sign test
• Percentile Wilcoxon signed rank test
• Ratio of percentiles
• Strength of lumber.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G15
• 62G30

Acknowledgments

The author thanks James Evans, United States Forest Products Laboratory, for providing the data for the example.