Date of Award
Master of Science (MS)
Mathematics and Statistics
Rex L. Hurst
Rex L. Hurst
In the past, tables have been published for the chi-square, t and F distributions. These tables have their own limitations with respect to the number of percentage points and degrees of freedom that are applicable. For instance, most tables for the chi-square distribution list tabular chi-square value for probabilities, .995, .99, .975, .95, .75, .5, .25, .1, .05, .025, .01, .005, .001, .0005, .0001 with degrees of freedom (1, 30, 1) and (40, 120, 10). However, suppose we want to know the chi-square value for probability .96 with degrees of freedom 10, or probability .95 with degrees of freedom 35; we would find other tables incomplete at this point. Besides, as the computer is getting widely used in research, it is worthwhile to have computer programs written to generate some of statistical functions rather than strictly to be limited by the tables.
Consequently, there have been methods developed to approximate chi-square, t and F value, when degrees of freedom and probability are known. It is the purpose of this study to present the methods of each individual distribution and evaluate its accuracy. Thus, the scope of this paper includes the following:
1. The definition and inverse function of each distribution.
2. The numerical approximate methods and examples.
3. A computer Fortran IV program to maximize the accuracy of calculation.
4. A comparison of the results obtained by numerical approximation with the known tabular value.
5. An evaluation of the capacity of these numerical methods.
Liang, Kuo-Chee, "Numerical Approximation to the Inverse Function of the Cumulative Chi-Square, t, and F Distribution" (1968). All Graduate Plan B and other Reports. 1109.
Copyright for this work is retained by the student. If you have any questions regarding the inclusion of this work in the Digital Commons, please email us at .