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International Journal Of Chemistry, Mathematics And Physics(IJCMP)

Bivariate normal-geometric distribution with FGM copula: Properties and parameter estimation

Sung-Hyon Ri , Hyon-A Kim , Kwang-Hyok Kim


International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-9,Issue-4, October - December 2025, Pages 13-27 , 10.22161/ijcmp.9.4.3

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Article Info: Received: 23 Sep 2025; Received in revised form: 19 Oct 2025; Accepted: 23 Oct 2025; Available online: 27 Oct 2025

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It is of practical importance to construct new effective statistical model for discrete and continuous data arising in the real world. The bivariate distribution with FGM copula whose two marginal distributions are normal and geometric, respectively, is proposed. The explicit characteristics and the moment generating function of the distribution are derived. Also, the conditional distributions and their characteristics of the distribution are obtained. The moment and maximum likelihood (ML) estimates for the parameters are investigated and the numerical results for them are presented. Real data analysis that indicates the usefulness of the model is also shown.

FGM copula, moment generating function, conditional distribution, moment estimation, ML estimation

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