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, for each fixed t≥0, it has a suitable multinomial conditional distribution of the components given their sum. In this paper we consider another multivariate process {M̲ν(t)=(M1 ν(t),…,Mm ν(t)):t≥0} 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 process ∑i=1 mMi ν(t):t≥0 coincide with the ones of the alternative fractional (univariate) Poisson process in Beghin and Macci (2013). We present large deviation results for {M̲ν(t)=(M1 ν(t),…,Mm ν(t)):t≥0}, 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 ν.

Asymptotic results for a multivariate version of the alternative fractional Poisson process / Beghin, Luisa; Macci, Claudio. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - STAMPA. - 129:(2017), pp. 260-268. [10.1016/j.spl.2017.06.009]

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

Beghin, Luisa;
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, for each fixed t≥0, it has a suitable multinomial conditional distribution of the components given their sum. In this paper we consider another multivariate process {M̲ν(t)=(M1 ν(t),…,Mm ν(t)):t≥0} 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 process ∑i=1 mMi ν(t):t≥0 coincide with the ones of the alternative fractional (univariate) Poisson process in Beghin and Macci (2013). We present large deviation results for {M̲ν(t)=(M1 ν(t),…,Mm ν(t)):t≥0}, 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 ν.
2017
first kind error probability; large deviations; moderate deviations; weighted Poisson distribution; statistics and probability; statistics, probability and uncertainty
01 Pubblicazione su rivista::01a Articolo in rivista
Asymptotic results for a multivariate version of the alternative fractional Poisson process / Beghin, Luisa; Macci, Claudio. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - STAMPA. - 129:(2017), pp. 260-268. [10.1016/j.spl.2017.06.009]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1020838
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