### Journals Information

Mathematics and Statistics Vol. 11(1), pp. 78 - 91
DOI: 10.13189/ms.2023.110109
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## A New Bivariate Odd Generalized Exponential Gompertz Distribution

Mervat Mahdy , Eman Fathy , Dina S. Eltelbany *
Faculty of Commerce, Benha University, Egypt

ABSTRACT

The objective of this study was to present a novel bivariate distribution, which we denoted as the bivariate odd generalized exponential gompertz(BOGE-G) distribution. Other well-known models included in this one include the gompertz, generalized exponential, odd generalized exponential, and odd generalized exponential gompertz distribution. The model introduced here is of Marshall-Olkin type [16]. The marginals of the new bivariate distribution have odd generalized exponential gompertz distribution which proposed by[7]. Closed forms exist for both the joint probability density function and the joint cumulative distribution function. The bivariate moment generating function, marginal moment generating function, conditional distribution, joint reliability function, marginal hazard rate function, joint mean waiting time, and joint reversed hazard rate function are some of the properties of this distribution that have been discussed. The maximum likelihood approach is used to estimate the model parameters. To demonstrate empirically the significance and adaptability of the new model in fitting and evaluating real lifespan data, two sets of real data are studied using the new bivariate distribution. Using the software Mathcad, a simulation research was conducted to evaluate the bias and mean square error (MSE) characteristics of MLE. We found that the bias and MSE decrease as the sample size increases.

KEYWORDS
Odd Generalized Exponential, Gompertz Distribution, Joint Probability Density Function, Conditional Probability Density Function, Maximum Likelihood Estimation, Fisher Information Matrix, Simulation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mervat Mahdy , Eman Fathy , Dina S. Eltelbany , "A New Bivariate Odd Generalized Exponential Gompertz Distribution," Mathematics and Statistics, Vol. 11, No. 1, pp. 78 - 91, 2023. DOI: 10.13189/ms.2023.110109.

(b). APA Format:
Mervat Mahdy , Eman Fathy , Dina S. Eltelbany (2023). A New Bivariate Odd Generalized Exponential Gompertz Distribution. Mathematics and Statistics, 11(1), 78 - 91. DOI: 10.13189/ms.2023.110109.