The theoretical analysis of the peak-to-average power ratio (PAPR) distribution for an orthogonal frequency division multiplexing (OFDM) system, depends on the particular waveform considered in the modulation system. In this paper,we generalize this analysis by considering the generalized waveforms for multi-carrier (GWMC) modulation systembased on any family of modulation functions, and we derive a general approximate expression for the cumulative distribution function (CDF) of its PAPR, for both finite and infinite integration time. These equations allow us to directlyfind the expressions of the PAPR distribution for any particular functions and characterize the behavior of the PAPRdistribution associated with different transmission and observation scenarios. In addition to that, a new approach to formulating the PAPR reduction problem as an optimization problem, is presented in this study.