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Some applications of probability generating function based methods to statistical estimation

Manuel L. Esquível — 2009

Discussiones Mathematicae Probability and Statistics

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...

Small perturbations with large effects on value-at-risk

Manuel L. Esquível;  Luís Dimas;  João Tiago Mexia;  Philippe Didier — 2013

Discussiones Mathematicae Probability and Statistics

We show that in the delta-normal model there exist perturbations of the Gaussian multivariate distribution of the returns of a portfolio such that the initial marginal distributions of the returns are statistically undistinguishable from the perturbed ones and such that the perturbed V@R is close to the worst possible V@R which, under some reasonable assumptions, is the sum of the V@Rs of each of the portfolio assets.

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