  A q-generalization of the product densities in stochastic point processes is
developed. The properties of these functions are studied and a q-generalization
of the usual $C^r_s$ coefficients is obtained. This for fixed q-number of
particles coincides with the q-Stirling numbers of the second kind. The
q-product densities are investigated using q-Poisson distribution and this
shows that the stochastic point processes involving consistent q-generalization
are inherently correlated. A closely related function to q-product densities is
a q-generalized Janossy function and a relation between the two is established.
