Recovery of a quantile function via moments

The main aim of this work is to construct accurate approximations of a quantile function Q under incomplete information upon the underlying distribution function (df) F . Namely, we assume that the only available data represent the values of a finite number of moments (‘‘cumulative frequency’’ moments, the Laplace transform) of F or Q. We propose two methods for approximation and estimation of a quantile function Q. The first method (method I) is based on the knowledge of the so-called ‘‘cumulative frequency’’ moments of F . The second one (method II) enables us to recover Q when only the integer order moments of F are known (or estimated) up to some order .