New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One

Muhammed Rasheed Irshad (), Sreedeviamma Aswathy, Radhakumari Maya and Saralees Nadarajah
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Muhammed Rasheed Irshad: Department of Statistics, Cochin University of Science and Technology, Cochin 682022, India
Sreedeviamma Aswathy: Department of Statistics, Cochin University of Science and Technology, Cochin 682022, India
Radhakumari Maya: Department of Statistics, University College, Thiruvananthapuram 695034, India
Saralees Nadarajah: Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

Mathematics, 2023, vol. 12, issue 1, 1-14

Abstract: Count data arise in inference, modeling, prediction, anomaly detection, monitoring, resource allocation, evaluation, and performance measurement. This paper focuses on a one-parameter discrete distribution obtained by compounding the Poisson and new X-Lindley distributions. The probability-generating function, moments, skewness, kurtosis, and other properties are derived in the closed form. The maximum likelihood method, method of moments, least squares method, and weighted least squares method are used for parameter estimation. A simulation study is carried out. The proposed distribution is applied as the innovation in an INAR(1) process. The importance of the proposed model is confirmed through the analysis of two real datasets.

Keywords: discrete statistical model; dispersion index; hazard rate function; parameter estimation; simulation; INAR(1) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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