This paper presents the relation between uncertainty in the excitation and parameters of vibrational energy harvesting systems and their power output. Nonlinear vibrational energy harvesters are very sensitive to the frequency of the base excitation. If the excitation frequency does not match with the resonance frequency of the energy harvester, the power output significantly deteriorates. The mismatch can be due to the inherent changes of the ambient oscillations. The fabrication errors or gradual changes of material properties also result in the mismatch. This paper quantitatively shows the probability density function for the power as a function of the probability densities of the excitation frequency, excitation amplitude, initial deflection of the energy harvester, and design parameters. Recently developed the conjugated unscented transformation methodology is used in conjunction with the principle of maximum entropy to compute the probability distribution for the base response and power. The computed nonlinear density functions are validated against Monte Carlo simulations.