Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications

Radhakumari Maya, Christophe Chesneau (), Anuresha Krishna and Muhammed Rasheed Irshad
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Radhakumari Maya: Department of Statistics, Government College for Women, Trivandrum 695 014, Kerala, India
Christophe Chesneau: Department of Mathematics, Université de Caen Basse-Normandie, F-14032 Caen, France
Anuresha Krishna: Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India
Muhammed Rasheed Irshad: Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India

Stats, 2022, vol. 5, issue 3, 1-18

Abstract: 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.

Keywords: extended exponential distribution; overdispersion; simulation; regression model; INAR(1) process (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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