By using a previously developed statistical model of the lightning discharge the probability density function for the initial peaks of the ground wave electric field generated by the return strokes was developed. The variation of the probability density function with the distance to the source is expressed analytically for the range of approximately 25–500 km in which the ground wave predominates. Since the statistical simulation model can include the frequency response of the receiving circuitry, the model can be used to predict the performance of threshold sensitive devices which operate on the initial peaks of the electric field. An example is given which illustrates the application of the results to a device similar to a lightning flash counter. Although only the induction and radiation field components were included in this study, it should be possible to modify the results to include the electrostatic component which would then allow calculation of the effective range of lightning flash counters.