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This work presents a novel two-parameter G family of continuous probability distributions with compounded parameters. To determine and examine the pertinent mathematical properties, calculations are performed. In one of the special sections, the standard inverse-Rayleigh baseline model is mathematically and statistically emphasized. We generated a number of bivariate and multivariate distributions using the copula method. These new distributions will aid in the modelling of bivariate and multivariate data. The applicability and flexibility of the new compounded two-parameters-G family are demonstrated through three applications to real-life data sets. These examples demonstrate the applicability of the family.
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