Extendibility of Marshall-Olkin distributions and inverse Pascal triangles

The class of infinitely extendible Marshall-Olkin distributions is characterized. A d-dimensional random vector (tau_1,...,tau_d)' on (Omega,F,P), following a Marshall-Olkin distribution, is parameterized by 2^d-1 parameters. A criterion on these parameters is given to decide whether or not there exists a sub-sigma-algebra G of F such that the random variables tau_1,...,tau_d are conditionally i.i.d. given G. This result makes use of the solution of the truncated Hausdorff's moment problem and a relation of the Marshall-Olkin distribution with inverse Pascal triangles.      «

The class of infinitely extendible Marshall-Olkin distributions is characterized. A d-dimensional random vector (tau_1,...,tau_d)' on (Omega,F,P), following a Marshall-Olkin distribution, is parameterized by 2^d-1 parameters. A criterion on these parameters is given to decide whether or not there exists a sub-sigma-algebra G of F such that the random variables tau_1,...,tau_d are conditionally i.i.d. given G. This result makes use of the solution of the truncated Hausdorff's moment problem and a...     »