Distributional Results for Means of Normalized Random Measures with Independent Increments

We consider the problem of determining the distribution of means of random probability measures which are obtained by normalizing increasing additive processes. A solution is found by resorting to a well-known inversion formula for characteristic functions due to Gurland. Moreover, expressions of th...

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Bibliographic Details
Published in:The Annals of statistics 2003-04, Vol.31 (2), p.560-585
Main Authors: Regazzini, Eugenio, Lijoi, Antonio, Prünster, Igor
Format: Article
Language:English
Subjects:
(normalized) random measure with independent increments
60G57
62F15
Adaptive Bayes Estimation and Distribution Theory
Approximation
Average linear density
Density distributions
Dirichlet process
Distribution functions
distribution of means of random probability measures
Exact sciences and technology
increasing addititive processes
Lévy measure
Mathematics
Parametric inference
Perceptron convergence procedure
Probabilities
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
Statistics
Stochastic processes
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Summary:We consider the problem of determining the distribution of means of random probability measures which are obtained by normalizing increasing additive processes. A solution is found by resorting to a well-known inversion formula for characteristic functions due to Gurland. Moreover, expressions of the posterior distributions of those means, in the presence of exchangeable observations, are given. Finally, a section is devoted to the illustration of two examples of statistical relevance.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1051027881