After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure by simulation and we prove the consistency of the estimator.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1111,
author = {Manuel L. Esqu\'\i vel},
title = {Some applications of probability generating function based methods to statistical estimation},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {29},
year = {2009},
pages = {131-153},
zbl = {1208.62028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1111}
}
Manuel L. Esquível. Some applications of probability generating function based methods to statistical estimation. Discussiones Mathematicae Probability and Statistics, Tome 29 (2009) pp. 131-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1111/
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