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In this paper, we propose a new statistical interference model for cognitive network based on the amplitude aggregate interference, which accounts for the parameters related to the sensing procedure, spatial reuse protocol employed by secondary users, and environment dependent conditions like channel fading and shadowing. We derive the characteristic function and the nth cumulant of the cognitive network interference on the primary user. By using the theory of truncated-stable distribution, we show how we can approximate the cognitive network interference analytically. We further show how to apply our model to derive system performance measure such as bit error probability in the presence of cognitive network interference. Moreover, this work can serve to bring additional understanding of cognitive network interference for successful deployment of cognitive networks in the future.