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There are many well-known bivariate distributions, such as the normal distribution, for which the question of whether they are max- or min-infinite divisible was settled a long time ago. However, despite its popularity, the bivariate Marshall–Olkin family of copulas was never the target of such an investigation, presumably due to the deterrent character of its density. Herein, we show that the challenges faced can be overcome with ease thanks to a convenient factorization.

Min-infinite divisibility of the bivariate Marshall–Olkin copulas