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<p>In this article, we propose an integer–valued autoregressive model of order one (INAR(1)) with a zero–one inflated negative binomial (ZOINB) innovation distribution based on binomial thinning. This model accounts for overdispersion and inflation at zero and one, making it highly adaptable for analyzing count data. We have derived essential statistical properties, including the conditional mean and variance. The study focuses on conditional maximum likelihood (CML) and expectation maximization (EM) estimation methods, which provide stable and reliable parameter estimates. Monte Carlo simulation studies confirm the accuracy and reliability of these estimation methods. The effectiveness of the proposed model is analyzed using the real–world public health datasets.</p>

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A Zero–One Inflated Negative Binomial INAR(1) Process

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • Aishwarya Ghodake,
  • Shrirang Pund,
  • Manik Awale

摘要

In this article, we propose an integer–valued autoregressive model of order one (INAR(1)) with a zero–one inflated negative binomial (ZOINB) innovation distribution based on binomial thinning. This model accounts for overdispersion and inflation at zero and one, making it highly adaptable for analyzing count data. We have derived essential statistical properties, including the conditional mean and variance. The study focuses on conditional maximum likelihood (CML) and expectation maximization (EM) estimation methods, which provide stable and reliable parameter estimates. Monte Carlo simulation studies confirm the accuracy and reliability of these estimation methods. The effectiveness of the proposed model is analyzed using the real–world public health datasets.