New Approach to Approximating the Cumulative Function for the t-Distribution

Section: Research Paper
Issue
Vol. 20 No. 2 (2023): Volume 20 Issue 2
Published
Jun 25, 2025
Pages
82-89

Abstract

The focus of this paper is to approximate the cumulative distribution function (CDF) of the t distribution, which represents a combined distribution of the normal distribution and gamma distribution. The study utilizes the approximate formula proposed by Polya for the normal distribution, originally introduced in 1945. By applying this final formula to various points and comparing the results with the tabulated values of the t distribution, the researchers found that the absolute error between the two sets of values is negligible. It should be noted that this error slightly increases with higher degrees of freedom. Furthermore, the study observed that the absolute errors remain consistent when multiple points are selected at the same degrees of freedom. These findings have practical implications for statistical analysis, as they offer a time and effort-saving approach for obtaining CDF values associated with the t-distribution.

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Authors

Ahmad Najem AL-SHALLAWI

Department of Statistics & Informative techniques, Northern Technical University, Mosul, Iraq.

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How to Cite

Najem AL-SHALLAWI, A., & احمد. (2025). New Approach to Approximating the Cumulative Function for the t-Distribution. IRAQI JOURNAL OF STATISTICAL SCIENCES, 20(2), 82–89. Retrieved from https://rjps.uomosul.edu.iq/index.php/stats/article/view/20646