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# Bivariate Gompertz generator of distributions: statistical properties and estimation with application to model football data

#### MS Eliwa,

##### College of Science, Majmaah University, Majmaah 11952, Saudi Arabia., SA
Department of Mathematics

#### ZA Alhussain,

##### College of Science, Majmaah University, Majmaah 11952, Saudi Arabia., SA
Department of Mathematics

#### EA Ahmed,

##### Taibah University, Community College of Khyber 41941, Saudi Arabia, SA
Department of Administrative and Financial Sciences

#### HH Ahmed,

##### Basic Science Department, College of Science, King Faisal University, Saudi Arabia., SA
Basic Science Department

#### M El- Morshedy

##### College of Sciences and Humanities Studies in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia, SA
Department of Mathematics

## Abstract

In this paper, the bivariate extension of the so called Gompertz-G family was introduced and studied in detail. Marshall and Olkin shock model was used to build the proposed bivariate family. The new family was constructed from three independent Gompertz-H families using a minimisation process. Some of its statistical properties such as joint probability density function, coefficient of median correlation, moments, product moment, covariance, conditional probability density function, joint reliability function, stress-strength reliability and joint reversed (hazard) rate function were derived. After introducing the general class, three special models of the new family were discussed. Maximum likelihood method was used to estimate the family parameters. A simulation study was carried out to examine the bias and mean square error of the maximum likelihood estimators. Finally, the importance of the proposed bivariate family was illustrated by means of real dataset, and it was found that the proposed model provides better fit than other well-known models in the statistical literature such as bivariate Gompertz, bivariate generalised Gompertz, bivariate Gumbel Gompertz, bivariate Burr X Gompertz and bivariate exponentiated Weibull-Gomperz.

##### Keywords: Bivariate distributions,Gompertz-H family of distributions,Marshall-Olkin shock model,maximum likelihood method
How to Cite: Eliwa, M., Alhussain, Z., Ahmed, E., Salah, M., Ahmed, H. and El- Morshedy, M., 2020. Bivariate Gompertz generator of distributions: statistical properties and estimation with application to model football data. Journal of the National Science Foundation of Sri Lanka, 48(2), pp.149–162. DOI: http://doi.org/10.4038/jnsfsr.v48i2.8779
Published on 13 Oct 2020.
Peer Reviewed