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In this paper, we study the outage capacity of amplify and forward (AF) multi-hop wireless communication systems over independent but not necessarily identical κ — μ fading channels. First, the probability density function (pdf) of the end to end signal to noise ratio (SNR) of the system is approximated as a weighted sum of Gaussian pdfs using the Gaussian finite mixture technique with expectation maximization. The approximated pdf is then utilized to derive a closed form expression for the outage capacity of the system in terms of a weighted sum of Q-functions. Numerical results show close agreement between simulation and analytical results.