A NEW CORRELATED BIVARIATE EXPONENTIAL DISTRIBUTION WITH APPLICATIONS.
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Abstract
The exponential distribution became the cornerstone of survival analysis and reliability engineering throughout the latter half of the 20th century and it is imperative to mention that the Successive times in exponential distribution are assumed to occur independently and randomly over time with a constant rate. The aim of the study was to develop a generalized and flexible bivariate exponential distribution that will incorporate correlation parameter 𝜌, extending the domain to a positive real-line using the framework of linear regression. A secondary dataset from Federal Road Safety Corps on road accidents in Imo State from 2020 to
2024 was used in the study and it was obtained from the Head office of Federal Road Safety Corps, off Egbu road Owerri, Imo state. In the study, we developed a generalized and bivariate exponential model that incorporates a correlation parameter, while preserving analytical simplicity. The proposed model, referred to as the New Correlated Bivariate Exponential Distribution (NCBED). The consistency of the NCBED was assessed using Kolmogorov Smirnov and Cramer Von Mises tests, in comparison with the baseline Grine model (2018). The Federal Road Safety (FRSC) dataset demonstrates that both injury and fatality data follow heavy-tailed exponential-type distributions and the NCBED provided a superior fit compared to the baseline model, capturing real-world correlations between crash outcomes. The findings indicate that the Maximum Likelihood estimates of the proposed model are consistent with the nature of the model.
2024 was used in the study and it was obtained from the Head office of Federal Road Safety Corps, off Egbu road Owerri, Imo state. In the study, we developed a generalized and bivariate exponential model that incorporates a correlation parameter, while preserving analytical simplicity. The proposed model, referred to as the New Correlated Bivariate Exponential Distribution (NCBED). The consistency of the NCBED was assessed using Kolmogorov Smirnov and Cramer Von Mises tests, in comparison with the baseline Grine model (2018). The Federal Road Safety (FRSC) dataset demonstrates that both injury and fatality data follow heavy-tailed exponential-type distributions and the NCBED provided a superior fit compared to the baseline model, capturing real-world correlations between crash outcomes. The findings indicate that the Maximum Likelihood estimates of the proposed model are consistent with the nature of the model.
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