On the interpolation of univariate distributions

This note discusses an interpolation technique for univariate distributions. In other words, the question is how to obtain a good approximation for f(x|a) if a0 < a < a1 is a control variable and f(x|a0) and f(x|a1) are known. The technique presented here is based on the interpolation of the quantile function, i.e. the inverse of the cumulative density function.