On Zero-Inflated Poisson Garima Distribution and its Applications to Count Data

Peer  Bilal Ahmad; Zehra  Skinder

Authors

Peer Bilal Ahmad Department of Mathematical Sciences, Islamic University of Science & Technology, Awantipura, Jammu and Kashmir, India
Zehra Skinder Department of Mathematical Sciences, Islamic University of Science & Technology, Awantipura, Jammu and Kashmir, India

Keywords:

Poisson Garima distribution, zero-inflated distribution, maximum likelihood estimation, goodness of fit, testing of hypothesis

Abstract

Excessive zero counts are one of the causes of over-dispersion in count data that is often observed in different fields. In this paper, we propose a new zero-inflated model namely ‘the zero-inflated Poisson Garima distribution’ to handle excessive zero counts. Various structural properties including reliability characteristics, generating functions, moments, etc. are obtained. Also, the parametric estimation of the proposed model is obtained using maximum likelihood method of estimation. Furthermore, a simulation study is carried out to check the behaviour of maximum likelihood estimators. Moreover, the proposed model and the baseline model are distinguished using two different test procedures. Finally, two real-life data sets taken from different domains are considered to validate the empirical applications of the proposed model.

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