## Distributional results for means of normalized random measures with independent increments.(English)Zbl 1068.62034

The authors consider random measures $$\tilde\phi$$ generated by increasing processes with independent increments using a time change. The introduced concept generalises Dirichlet random probability measures that are obtained using a time change of a reparametrised gamma-subordinator whose increments follow the gamma distribution. An expression for the distribution of the mean of the introduced random measure is found by using the Gurland inversion formula for characteristic functions.
Given a sample $$X_1,\dots,X_n$$ of random variables, conditionally i.i.d. given the random measure $$\tilde\phi$$ and distributed according to $$\tilde\phi$$, the authors derive an expression for the posterior distribution of the mean of $$\tilde\phi$$ which is useful for the Bayesian inference. A lengthy final section presents two examples of statistical relevance.

### MSC:

 62F15 Bayesian inference 60G57 Random measures 60G51 Processes with independent increments; Lévy processes
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### References:

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LIJOI I. PRÜNSTER DIPARTIMENTO DI ECONOMIA POLITICA E METODI QUANTITATIVI UNIVERSITÀ DEGLI STUDI DI PAVIA VIA SAN FELICE, 5 27100 PAVIA ITALY E-MAIL: lijoi@unipv.it igor.pruenster@unipv.it
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