×

Some applications of probability generating function based methods to statistical estimation. (English) Zbl 1208.62028

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.

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)
PDFBibTeX XMLCite
Full Text: DOI