We re-constructed the formula of the probability density function (pdf) and the cumulative distribution function (cdf) for the bivariate t distribution. Both the formulae for pdf and cdf of the bivariate t distributions are manually re-constructed. The R-code is then used to graphically analyze pdf on several parameters, and to compute the values of the cdf.

To simulate the computation of the values of the cdf, we used several degrees of freedom (df) such as 1, 5, and 10. The results show that the values of the pdf increase as both correlation coefficient and degree  of freedom increase. The peaks of the pdf curves occur when the correlation coefficient is 0.5. The value of the cdf is greater than 0.90 (close to be one) when the df happened to be 5 and 10.

bivariate t distribution, cdf, graphs, pdf, R-code.

Received: July 8, 2024; Revised: August 18, 2024; Accepted: August 27, 2024; Published: September 6, 2024

How to cite this article: Budi Pratikno, Debora Sukabhakti and Siti Khotijah, The bivariate t distribution and its graphical analysis, Universal Journal of Mathematics and Mathematical Sciences 20(2) (2024), 153-161. https://doi.org/10.17654/2277141724009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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