Linear interpolation of histograms

A prescription is defined for the interpolation of probability distributions that are assumed to have a linear dependence on a parameter of the distributions. The distributions may be in the form of continuous functions or histograms. The prescription is based on the weighted mean of the inverses of the cumulative distributions between which the interpolation is made. The result is particularly elegant for a certain class of distributions, including the normal and exponential distributions, and is useful for the interpolation of Monte Carlo simulation results which are time-consuming to obtain.