A continuous estimator of a distribution function that reproduces the empirical moments
Jacques F. Carriére · Communication in Statistics- Theory and Methods · 1993
Suppose we have a random sample from a continuous distribution function with support on the positive reals. This paper will investigate a semi-parametric estimator of the distribution function that is based on mixtures of lognormal distributions. This estimator will be constructed so that a specified number of moments of the empirical distribution function are reproduced. We will give several asymptotic results for this moment-type estimator including a central limit theorem.