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 generalized Gompertz, bivariate
Gumbel Gompertz, bivariate Burr X Gompertz and bivariate
exponentiated Weibull-Gomperz