A multivariate fractional Poisson process was recently defined in Beghin and Macci (2016) by considering a common independent random time change for a finite dimensional vector of independent (non-fractional) Poisson processes; moreover it was proved that it has suitable multinomial conditional distributions of the components given their sum. In this paper we consider another multivariate process with the same conditional distributions of the components given their sums, and different marginal distributions of the sums; more precisely we assume that the one-dimensional marginal distributions of the sum-process coincide with the ones of the alternative fractional (univariate) Poisson process in Beghin and Macci (2013). We present large deviation results, and this generalizes the result in Beghin and Macci (2013) concerning the univariate case. We also study moderate deviations and we present some statistical applications concerning the estimation of the fractional parameter.

Beghin, L., & Macci, C. (2017). Asymptotic results for a multivariate version of the alternative fractional Poisson process. STATISTICS & PROBABILITY LETTERS, 129, 260-268 [10.1016/j.spl.2017.06.009].

Asymptotic results for a multivariate version of the alternative fractional Poisson process

MACCI, CLAUDIO
2017

Abstract

A multivariate fractional Poisson process was recently defined in Beghin and Macci (2016) by considering a common independent random time change for a finite dimensional vector of independent (non-fractional) Poisson processes; moreover it was proved that it has suitable multinomial conditional distributions of the components given their sum. In this paper we consider another multivariate process with the same conditional distributions of the components given their sums, and different marginal distributions of the sums; more precisely we assume that the one-dimensional marginal distributions of the sum-process coincide with the ones of the alternative fractional (univariate) Poisson process in Beghin and Macci (2013). We present large deviation results, and this generalizes the result in Beghin and Macci (2013) concerning the univariate case. We also study moderate deviations and we present some statistical applications concerning the estimation of the fractional parameter.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - Probabilita' e Statistica Matematica
English
Beghin, L., & Macci, C. (2017). Asymptotic results for a multivariate version of the alternative fractional Poisson process. STATISTICS & PROBABILITY LETTERS, 129, 260-268 [10.1016/j.spl.2017.06.009].
Beghin, L; Macci, C
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/186477
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