Farlie-Gumbel-Morgenstern bivariate log-normal: applications and comparison of semiparametric and parametric methods for estimating copulas

This study introduces the Farlie-Gumbel-Morgenstern bivariate log-normal (bivariate FGM-LN) distribution, which was created using the FGM copula to describe dependent skewed data. The copula probability density function (PDF) and the cumulative density function (CDF) plots are used to study the distribution's behavior, revealing its ability to capture varying dependency patterns. Simulation research compares parameter estimating approaches, revealing that MLE provides the highest accurate estimates, inference function for margins (IFM) is more computationally efficient, and semiparametric (SP) stays resilient but requires larger sample numbers. Furthermore, Kolmogorov-Smirnov (KS) statistics are also used on real-life recurrence time data from 30 patients to determine the goodness-of-fit for the marginal distributions and validate the model's suitability. The model selection criteria confirm that bivariate FGM-LN outperforms the existing models, with the lowest AIC and BIC scores. The findings emphasize the bivariate FGM-LN distribution's applicability in dependability modeling, survival analysis, and risk assessment, providing a statistically sound alternative to bivariate dependency modeling.