Recovery of a quantile function from moments

摘要

The problem of recovering a quantile function of a positive random variable via the values of moments or given the values of its Laplace transform is studied. Two new approximations as well as two new estimates of a quantile function given the sample from underlying distribution are proposed. The uniform and L1 upper bounds of proposed estimates are derived. The plots illustrate the behavior of the recovered approximants for the moderate and large sample sizes.