| Title |
On the Bivariate Extension of the Extended Standard U-quadratic Distribution |
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Authors |
Idzhar Lakibul, Daisy Lou Polestico, Arnulfo Supe |
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Publication date |
2024-04-30 |
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Journal |
European Journal of Pure and Applied Mathematics |
| Volume |
Volume 17 |
| Issue |
No. 2 |
| Pages |
790-809 |
| Publisher |
New York Business Global, Maryland, USA |
| Abstract |
This paper derives the bivariate version of the extended standard U-quadratic (eSU) distribution using the method of compounding or pseudo family of distributions. The joint probability and cumulative distribution functions of the derived distribution are obtained and it is observed that the said distribution can generate bivariate shape with the following properties: (i) X and Y have bathtub shapes; (ii) X has constant and Y has bathtub shapes; and (iii) X has inverted bathtub and Y has bathtub shapes. Moreover, some properties of the derived distribution such as the marginal distribution, conditional distributions, conditional moments, product and ratio moments are derived. Further, the maximum likelihood estimation is performed to estimate the parameters of the derived distribution. Also, a simulation study is carried out to evaluate the behavior of the estimates of the parameters. Moreover, we derive a new bivariate Kumaraswamy distribution and use it to simulate bivariate data with X and Y having bathtub shapes. Furthermore, A new bivariate version of the Cubic Transmuted Uniform (CTU) distribution is also derived. Finally, the proposed Bivariate eSU distribution is applied to simulated data and compared with the said Bivariate Cubic Transmuted Uniform distribution. The result shows that the proposed Bivariate eSU distribution provides a better fit for the said simulated dataset as compared with the Bivariate CTU distribution. |
| Index terms / Keywords |
Standard U-quadratic distribution, Kumaraswamy distribution, Bivariate distribution, Bivariate Pseudo Family, bathtub shape distribution |
| DOI |
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| URL |
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Mindanao State
University - Iligan Institute of Technology