Poisson Xgamma distribution: A discrete model for count data analysis

Article type: Research Article

Authors: Para, Bilal Ahmad^{a; *} | Jan, Tariq Rashid^b | Bakouch, Hassan S.^c

Affiliations: [a] Department of Statistics, Government Degree College Boys Anantnag, India | [b] Department of Statistics, University of Kashmir, Srinagar, India | [c] Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Correspondence: [*] Corresponding author: Bilal Ahmad Para, Department of Statistics, Government Degree College Boys Anantnag (J&K), India. Tel.: +91 7006384470; E-mail: parabilal@gmail.com.

Abstract: In this article, we attempt to introduce a count data model which is obtained by compounding Poisson distribution with Xgamma distribution. Important mathematical and statistical properties of the distribution have been derived and discussed. Parameter estimation is discussed using the maximum likelihood method of estimation followed by Monte Carlo simulation to investigate the behavior of the ML estimators. Finally, two real-life data sets are analyzed to investigate the suitability of the proposed distribution in modeling count data.

Keywords: Poisson distribution, Xgamma distribution, compounding, count data

DOI: 10.3233/MAS-200484

Journal: Model Assisted Statistics and Applications, vol. 15, no. 2, pp. 139-151, 2020