Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications
1
Department of Statistics, Government College for Women, Trivandrum 695 014, Kerala, India
2
Department of Mathematics, Université de Caen Basse-Normandie, F-14032 Caen, France
3
Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India
*
Author to whom correspondence should be addressed.
Academic Editor: Wei Zhu
Stats 2022, 5(3), 755-772; https://doi.org/10.3390/stats5030044
Received: 8 July 2022
/
Revised: 23 July 2022
/
Accepted: 3 August 2022
/
Published: 5 August 2022
The significance of count data modeling and its applications to real-world phenomena have been highlighted in several research studies. The present study focuses on a two-parameter discrete distribution that can be obtained by compounding the Poisson and extended exponential distributions. It has tractable and explicit forms for its statistical properties. The maximum likelihood estimation method is used to estimate the unknown parameters. An extensive simulation study was also performed. In this paper, the significance of the proposed distribution is demonstrated in a count regression model and in a first-order integer-valued autoregressive process, referred to as the INAR(1) process. In addition to this, the empirical importance of the proposed model is proved through three real-data applications, and the empirical findings indicate that the proposed INAR(1) model provides better results than other competitive models for time series of counts that display overdispersion.
View Full-Text
Keywords:
extended exponential distribution; overdispersion; simulation; regression model; INAR(1) process
▼
Show Figures
Figure 1
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
MDPI and ACS Style
Maya, R.; Chesneau, C.; Krishna, A.; Irshad, M.R. Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications. Stats 2022, 5, 755-772. https://doi.org/10.3390/stats5030044
AMA Style
Maya R, Chesneau C, Krishna A, Irshad MR. Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications. Stats. 2022; 5(3):755-772. https://doi.org/10.3390/stats5030044
Chicago/Turabian StyleMaya, Radhakumari, Christophe Chesneau, Anuresha Krishna, and Muhammed Rasheed Irshad. 2022. "Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications" Stats 5, no. 3: 755-772. https://doi.org/10.3390/stats5030044
Find Other Styles
