Central limit theorem, modern extreme value theory and the theory that the discrete orthogonal frequency division multiplexing signals converge weakly to a Gaussian random process are generally employed to derive the best approximation of peak-to-average power ratio distributions of discrete-time and continuous-time signals. In this paper, we arrive at a simple, rigorously justified, and accurate expression of the upper bound of the probability density function of the PAPR in context of orthogonal frequency division multiplexing systems. Since this bound has a complex expression not convenient to deal with in practice, we show also the demonstration of an accurate estimation of the proposed bound.