Efficient computation of the distribution functions of student's t chi-squared and fto moderate accuracy

Abstract

Ling (1978) recently reported on the accuracy of some approximations to the tail areas of F, chi-squared and F to help design efficient and moderately (3 to 5 decimal places) accurate programs for these probabilities. This paper examines two further approximations, and stresses the need for careful coding if one is to avoid loss of accuracy in single precision implementations on short word length computers. With careful coding five decimal places can easily be obtained for t and chi-squared probabilities, while for t four places are obtainable with reasonable computational effort.

Keywords:

• Algorithms
• approximations
• Cornish-Fisher expansions
• numerical accuracy
• short word length
• single precision

^†Supported by the Fund for Research, Teaching, Department of Nutrition, Harvard School of Public Health.

^†Supported by the Fund for Research, Teaching, Department of Nutrition, Harvard School of Public Health.

Notes

^†Supported by the Fund for Research, Teaching, Department of Nutrition, Harvard School of Public Health.