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Titre du document / Document title

A class of correlated weighted Poisson processes

Auteur(s) / Author(s)

BORGES P. (1) ; RODRIGUES J. (2) ; BALAKRISHNAN N. (3) ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

(1) Departamento de Estatistica, Universidade do Espirito Santo - UFES. Av. Fernando Ferrari 514, Goiabeiras, CEP 29075-910 Vitøria ES, BRESIL
(2) Departamento de Estatística, Universidade de São Carlos, BRESIL
(3) Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, CANADA

Résumé / Abstract

In this paper, we propose new classes of correlated Poisson processes and correlated weighted Poisson processes on the interval [0,1], which generalize the class of weighted Poisson processes defined by Balakrishnan and Kozubowski (2008), by incorporating a dependence structure between the standard uniform variables used in the construction. In this manner, we obtain another process that we refer to as correlated weighted Poisson process. Various properties of this process such as marginal and joint distributions, stationarity of the increments, moments, and the covariance function, are studied. The results are then illustrated through some examples, which include processes with length-biased Poisson, exponentially weighted Poisson, negative binomial, and COM-Poisson distributions.

Revue / Journal Title

Journal of statistical planning and inference    ISSN  0378-3758   CODEN JSPIDN 

Source / Source

2012, vol. 142, no1, pp. 366-375 [10 page(s) (article)] (1/4 p.)

Langue / Language

Anglais

Editeur / Publisher

Elsevier, Kidlington, ROYAUME-UNI  (1977) (Revue)

Mots-clés anglais / English Keywords

Covariance function

;

Correlation coefficient

;

Negative binomial distribution

;

Biased estimation

;

Length weight relation

;

Statistical moment

;

Joint distribution

;

Marginal distribution

;

Poisson process

;

Correlation analysis

;

Approximation theory

;

Statistical distribution

;

Statistical decision

;

Statistical method

;

Mots-clés français / French Keywords

Fonction covariance

;

62E17

;

Coefficient corrélation

;

Loi binomiale négative

;

Estimation biaisée

;

Relation poids taille

;

Moment statistique

;

Loi conjointe

;

Loi marginale

;

Processus Poisson

;

Analyse corrélation

;

Théorie approximation

;

Distribution statistique

;

Décision statistique

;

Méthode statistique

;

Mots-clés espagnols / Spanish Keywords

Coeficiente correlación

;

Ley binomial negativa

;

Estimación sesgada

;

Relación peso tamaño

;

Momento estadístico

;

Ley conjunta

;

Ley marginal

;

Proceso Poisson

;

Análisis correlación

;

Distribución estadística

;

Decisión estadística

;

Método estadístico

;

Mots-clés d'auteur / Author Keywords

Correlated Poisson process on [0,1]

;

Standard uniform variables

;

Exchangeable variables

;

Correlation coefficient

;

Correlated weighted Poisson process

;

Localisation / Location

INIST-CNRS, Cote INIST : 17575, 35400050997510.0310

Nº notice refdoc (ud4) : 24579425



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