Summary
A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function.
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Work performed while the authors were members of CNR-GNAFA.
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Muliere, P., Scarsini, M. Characterization of a Marshall-Olkin type class of distributions. Ann Inst Stat Math 39, 429–441 (1987). https://doi.org/10.1007/BF02491480
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DOI: https://doi.org/10.1007/BF02491480