A Viable Alternative to Resorting to Statistical Tables

Abstract

It is shown in this article that, given the moments of a distribution, any percentage point can be accurately determined from an approximation of the corresponding density function in terms of the product of an appropriate baseline density and a polynomial adjustment. This approach, which is based on a moment-matching technique, is not only conceptually simple but easy to implement. As illustrated by several applications, the percentiles so obtained are in excellent agreement with the tabulated values. Whereas statistical tables, if at all available or accessible, can hardly ever cover all the potentially useful combinations of the parameters associated with a random quantity of interest, the proposed methodology has no such limitation.

Keywords:

• Approximate distributions
• Computational statistics
• Moments
• Percentage points
• Percentiles
• p-values
• Statistical tables

Mathematics Subject Classification:

• Primary 60E17, 62Q05
• Secondary 62H10

Acknowledgments

The financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. The authors also wish to express their sincere thanks to a referee for valuable suggestions that significantly improved the presentation of the material.