Some results for moment-empirical cumulative distribution functions

Abstract

An unknown probability cumulative distribution function (CDF) can be recovered from its moments and estimated from its empirical moments. In this paper, some further results for such moment-empirical CDFs’ are considered, in particular for certain models where the sample is not directly drawn from the distribution of actual interest, as in biased sampling.

Keywords:

• Moment-empirical CDF
• Biased sampling model
• Weak convergence
• Construction of the limiting process

Acknowledgement

We would like to thank the Editor and a referee for valuable comments and suggestions. Work partially supported by INTAS-Georgia 97-1828 grant and Georgian Academy of Sciences grant 1.10.02.