4.2 Article

Modeling Medical Data by Flexible Integer-Valued AR(1) Process with Zero-and-One-Inflated Geometric Innovations

Publisher

SPRINGER INT PUBL AG
DOI: 10.1007/s40995-022-01297-3

Keywords

INAR process; Geometric distribution; Zero-and-one-inflated geometric distribution; Binomial thinning operator; Estimation; Runs

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This paper introduces a new stationary first-order integer-valued autoregressive process (INAR) with zero-and-one-inflated geometric innovations, which is useful for modeling medical practical data. The basic probabilistic and statistical properties of the model are discussed. The proposed model is applied to analyze two medical series and compared with other competing models based on goodness-of-fit statistics and selection criteria.
In this paper, we introduce a new stationary first-order integer-valued autoregressive process (INAR) with zero-and-one-inflated geometric innovations that is useful for modeling medical practical data. Basic probabilistic and statistical properties of the model are discussed. Conditional least squares and maximum likelihood estimators are proposed to estimate the model parameters. The performance of the estimation methods is assessed by some Monte Carlo simulation experiments. The zero-and-one-inflated INAR process is subsequently applied to analyze two medical series that include the number of new COVID-19-infected series from Barbados and Poliomyelitis data. The proposed model is compared with other popular competing zero-inflated and zero-and-one-inflated INAR models on the basis of some goodness-of-fit statistics and selection criteria, where it shows to provide better fitting and hence can be considered as another important commendable model in the class of INAR models.

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