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The peak to average power ratio (PAPR) reduction performance depends on the phase vectors of selected mapping (SLM) scheme where the alternative input symbol vectors are generated by multiplying an input symbol vector by phase vectors. Thus, the symbol powers of alternative orthogonal frequency division multiplexing (OFDM) signals obtained by inverse Fourier transforming the alternative input symbol vectors become correlated. In this paper, the relationship between the correlations of component powers of alternative OFDM signal vector and the correlations of phase vectors are evaluated. Then, the complementary cumulative distribution function (CCDF) of PAPR in SLM scheme is derived using multivariate gamma distribution. The derived CCDF coincides exactly with the simulation result for peak reduced OFDM system with SLM.