Esquível, Manuel L. Some applications of probability generating function based methods to statistical estimation. (English) Zbl 1208.62028 Discuss. Math., Probab. Stat. 29, No. 2, 131-153 (2009). Summary: 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. Cited in 1 Document MSC: 62F10 Point estimation 60E10 Characteristic functions; other transforms 62G05 Nonparametric estimation 60F15 Strong limit theorems 60F17 Functional limit theorems; invariance principles 65C60 Computational problems in statistics (MSC2010) Keywords:empirical laws; estimation of parameters of continuous laws PDFBibTeX XMLCite \textit{M. L. Esquível}, Discuss. Math., Probab. Stat. 29, No. 2, 131--153 (2009; Zbl 1208.62028) Full Text: DOI