  When the distribution of a random (N) sum of independent copies of a r.v X is
of the same type as that of X we say that X is N-sum stable. In this paper we
consider a generalization of stability of geometric sums by studying
distributions that are stable under summation w.r.t Harris law. We show that
the notion of stability of random sums can be extended to include the case when
X is discrete. Finally we propose a method to identify the probability law of N
for which X is N-sum stable. See also Satheesh and Nair (2002), (Some classes
of distributions on ther non-negative lattice, J. Ind. Statist. Assoc., 2002,
40, 41-58) for a study of discrete laws of the same type and stability of
geometric sums of discrete laws.
