Abstract
Evaluation of probability distribution functions and their inverse functions plays a primarily important role in a statistical analysis and inference. In addition to statistically critical values, it produces probability values required to complete such inferential tasks. Therefore Chi-squared (X2) distribution function was evaluated via its related incomplete gamma function and by integrating the power series and continued fraction expansion with the left-to-right and right-to-left approaches. The standard normal z, Student's t, F, and X2 values were computed using the step number-skipping and binary bisection search. With the optimized algorithm and a computer-based convergence technique as well as their simplicity, they resulted in a tremendous improvement of computational precision and efficiency. Other novel notion and important information on integrating probability distribution functions with computing tricks has also been introduced.
Published Version
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