For meaningful co-existence of cognitive radios with primary system, it is imperative that the cognitive radio system is aware of how much interference it generates at the primary receivers. This can be done through statistical modeling of the interference as perceived at the primary receivers. In this work, we propose a generalized model for the interference generated by a cognitive radio network, in the presence of small and large scale fading, at a primary receiver located at the origin. We then demonstrate how this model can be used to estimate the impact of cognitive radio transmission on the primary receiver in terms of different outage probabilities. Finally, our analytical findings are validated through some selected computer-based simulations.