Abstract
The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We establish and prove the following results: to an arbitrary degree of accuracy, (a) location-scale mixtures of a continuous probability density function (PDF) can approximate any continuous PDF, uniformly, on a compact set; and (b) for any finite location-scale mixtures of an essentially bounded PDF can approximate any PDF in
in the
norm.
MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors would like to very much thank Pr. Eric Ricard for the interesting discussions with him and for his suggestions.