This paper presents the analysis and design of a dynamic inductive power transfer (IPT) system, in which coupling is treated as a stochastic variable and is therefore modelled as a probability distribution. The purpose of this formulation is to optimise the tuning of the inverter and the rectifier to the coupling value that achieves the highest charging energy-efficiency when operating at a broad range of coupling. The analysis is supported by a case study in which two rectifier designs, using the hybrid Class E topology, are tuned at different coupling values in order to verify which version achieves the highest charging efficiency. The load in the experiments is a wirelessly powered drone without a battery hovering randomly over the charging pad, and the range of motion is set by a nylon string tether. The experiments show lower energy consumption when the rectifier is tuned to present the optimal load of the link at the coupling value with the highest probability, as opposed to the first, which was designed to present the optimal load of the link at minimum coupling.