Bivariate power Lomax Sarmanov distribution: Statistical properties, Reliability measures, and Parameter estimation

This paper presents a bivariate power Lomax Sarmanov distribution (BPL-SARD) constructed from Sarmanov copulas and power Lomax (PL) marginal distributions. For modeling bivariate life expectancy data, this model provides a significant lifetime distribution. Several statistical properties of the BPL-SARD are derived and discussed, such as marginal distributions, product moments, coefficients of correlation between the inner variables, conditional distributions, conditional expectations, moment-generating functions, and the positive quadrant dependence property. We also obtained reliability measures, such as survival function, hazard rate function, mean residual life function, and vitality function. Model parameters are estimated using the maximum likelihood (ML) and Bayesian methods. Moreover, we derive asymptotic confidence intervals for the parameter model. To assess the effectiveness of both ML and Bayesian estimators, Monte Carlo simulation analysis is used. Furthermore, bootstrap confidence intervals were computed. Finally, two real data sets are analyzed to demonstrate the practical application of the proposed model. Because the Sarmanov copula is completely superior to all copulas that generalize the FGM copula, the BPL-SARD distribution performs better than any other bivariate PL distribution based on the FGM copula and its generalizations, which is the uniqueness and significance of this research.