The statistical behavior of wave energy at a single site is derived by considering simultaneous variations in the period and wave height. In this paper, the general wave power formulation is derived by using the theory of perturbation. This method leads to a general formulation of the wave power expectation and other statistical parameter expressions, such as standard deviation and coefficient of variation. The statistical parameters, namely the mean value and variance of wave energy, are found in terms of the simple statistical parameters of period, significant wave height and zero up-crossing period. The elegance of these parameters is that they are distribution free. These parameters provide a means for defining the wave energy distribution function by employing the Chebyschev's inequality. Subsequently, an approximate probability distribution function of the wave energy is also derived for assessment of risk and reliability associated with wave energy. Necessary simple charts are given for risk and reliability assessments. Two procedures are presented for such assessments in wave energy calculations and the applications of these procedures are provided for wave energy potential assessment in the regions of the Pacific Ocean off the west coast of U.S. © 2003 Elsevier Ltd. All rights reserved.