On the interpolation of univariate distributions

TL;DR

This paper introduces an interpolation method for univariate distributions by interpolating their quantile functions, enabling approximation of distributions between known endpoints based on a control variable.

Contribution

It proposes a novel interpolation technique for univariate distributions using quantile functions, providing a new approach for distribution approximation.

Findings

Effective interpolation of distributions via quantile functions.

Applicable for estimating distributions between known points.

Potential for improved distribution modeling in statistical analysis.

Abstract

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.