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Abstract
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The primary objective of this article was to introduce a new probabilistic model for the dis-
cussion and analysis of random covariates. The introduced model was derived based on the Marshall–
Olkin shock model. After proposing the mathematical form of the new bivariate model, some of its
distributional properties, including joint probability distribution, joint reliability distribution, joint
reversed (hazard) rate distribution, marginal probability density function, conditional probability
density function, moments, and distributions for bothY = max{X1,X2} andW = min{X1,X2}, were
investigated. This novel model can be applied to discuss and evaluate symmetric and asymmetric
data under various kinds of dispersion. Moreover, it can be used as a probability approach to analyze
different shapes of hazard rates. The maximum likelihood approach was utilized for estimating the
parameters of the bivariate model. A simulation study was carried out to assess the performance of
the parameters, and it was noted that the maximum likelihood technique can be used to generate
consistent estimators. Finally, two real datasets were analyzed to illustrate the notability of the novel
bivariate distribution, and it was found that the suggested distribution provided a better fit than the
competitive bivariate models.
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