Small antennas installed on large structures can be critical elements which need to be fully characterized radiation wise. Such an issue naturally arises for airborne antennas for example. This paper presents a crucial step in the modeling of such a radiation in a complex environment. Considering a patch antenna installed on an infinite cylinder, its radiation is analyzed while taking into account variability in the antenna parameters, as well as in the cylinder geometry. By the Polynomial Chaos Expansion of the analytical field, the resulting stochastic radiation pattern can be derived to quantify uncertainty and thus bound the possible realizations of the antenna radiation with respect to variable parameters.