Proposed empirical relationships between frequency dependent complex electrical resistivity and key physical properties, such as grain or pore throat size, may allow hydraulic conductivity to be indirectly estimated from variable frequency electrical measurements, often referred to as spectral induced polarization (SIP). The SIP response may be described by several models, each providing one or more estimated values of relaxation time and chargeability, and a variety of additional parameters. Recent interest has been shown in modelling the SIP response as the coupling of a large number of simple Debye responses, each fully described by the two parameters of relaxation time and chargeability, and with no requirement for additional model parameters. This deterministic approach allows the SIP response to be matched with high accuracy, but since the mean, mode and median relaxation times of the total chargeability may differ widely, none of these statistics is sufficient to summarise the SIP response adequately. We introduce a parsimonious set of descriptors which efficiently summarises the distribution of Debye relaxations, with minimal loss of the information content in the electrical measurements. Our method applies a Markov chain Monte Carlo algorithm to provide a Bayesian estimation of the relaxation distribution parameters, and does not require an accurate prior estimation of DC resistivity. The distribution parameters may be combined with electrical-physical relationships identified in other studies, to give stochastic estimates of hydraulic conductivity. We apply our approach to electrical spectra measured in the laboratory and in field surveys, and we compare our results with those from deterministic methods.