Abstract
We introduce a new bivariate probability distribution, termed the Bivariate FGM Type-2 Gumbel Distribution, constructed by combining the Farlie–Gumbel–Morgenstern (FGM) copula with the Type-2 Gumbel marginal distributions. This proposed distribution provides a flexible framework for modeling bivariate data and offers a viable alternative to several existing bivariate distributions, especially in scenarios where capturing dependence between variables is crucial. The theoretical properties of the distribution are thoroughly explored. We derive the marginal and conditional distributions, conditional expectations, moment generating function, and product moments. Procedures for random number generation from the distribution are discussed. Reliability-based characteristics, such as the survival function and hazard function, are also formulated, enhancing the applicability of the model in reliability analysis and life data modeling. For parameter estimation, we employ the maximum likelihood estimation (MLE) technique, and the estimators’ performance is examined through a comprehensive simulation study. To demonstrate practical utility, the proposed distribution is applied to a real-world dataset, where it shows a good fit and provides insightful results, underscoring its relevance for applied statistical modeling.
Recommended Citation
Javed, Muneeb; Shah, Said Farooq; Osama, Muhammad; Atif, Muhammad; and Farooq, Muhammad
(2025).
(R2152) New Bivariate Type-2 Gumbel Distribution Based on the Farlie-Gumbel-Morgenstern Copula: Properties and its Application in Survival Analysis,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 20,
Iss.
2, Article 6.
Available at:
https://digitalcommons.pvamu.edu/aam/vol20/iss2/6