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 line
x=
y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function.
Key words and phrases Characterization - functional equation - Marshall-Olkin distribution - lack of memory property - copula
Work performed while the authors were members of CNR-GNAFA.