An extended Poisson distribution

Hassan Bakouch (1) , Maher Kachour (2) , Saralees Nadarajah (3)

1 Department of Statistics, Faculty of Sciences, King Abdulaziz University, Jeddah
2 IDRAC Business school Lyon - Institut pour le Développement et la Recherche d'Action Commerciale
3 School of Mathematics - Department of Mathematics [Manchester]

The Poisson distribution is extended over the set of all integers. The motivation comes from the many reflected versions of the gamma distribution, the continuous analog of the Poisson distribution, defined over the entire real line. Various mathematical properties of the extended Poisson distribution are derived. Estimation procedures by the methods of moments and maximum likelihood are also derived with their performance assessed by sim- ulation. Finally, a real data application is illustrated.

Mots clés: Poisson distribution; Skellam distribution

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Hassan Bakouch, Maher Kachour, Saralees Nadarajah. An extended Poisson distribution. 2013. ⟨hal-00959426⟩