A New First-Order Integer-Valued Autoregressive Model with Bell Innovations

Huang, Jie; Zhu, Fukang

doi:10.3390/e23060713

Cited by 19 publications

(10 citation statements)

References 31 publications

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“…Pioneer works dealing with an INAR(1) process with Poisson innovations were given by McKenzie (1985) and Al-Osh and Alzaid (1987). Subsequently, in order to model both overdispersed and underdispersed count data, several INAR(1) models with different innovation processes have been introduced in the statistical literature, such as the INAR(1)G with geometric innovations (Aghababaei Jazi et al (2022)), INAR(1)PQX with Poisson quasi-xgamma innovations (Altun et al (2021)), INAR(1)BL with Bell innovations (Huang and Zhu (2021)) and INAR(1)DB with Bilal innovations (Altun et al (2022)), among others.…”

Section: Introductionmentioning

confidence: 99%

The discrete new XLindley distribution and the associated autoregressive process

Maya,

Jodrá,

Aswathy

et al. 2024

Int J Data Sci Anal

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The continuous new XLindley distribution was introduced by Nawel et al. ( 2023) as a special case of the polynomial exponential distribution proposed by Beghriche et al. (2022). The current paper introduces the one-parameter discrete analogue distribution of the new XLindley model and studies its main statistical properties. In particular, closed-form expressions are provided for the moment generating function, mean, variance, quantile function, hazard rate function and mean residual life. Moreover, the new distribution has discrete increasing failure rate and both overdispersed and underdispersed count data can be handled. The estimation of the unknown parameter can be performed by the maximum likelihood method and a Monte Carlo simulation study reveals that this method provides satisfactory estimates. Additionally, a Ąrst-order integer-valued autoregressive process is constructed from the discrete distribution and, via a simulation study, the conditional maximum likelihood method is recommended for estimation purposes. In order to assess the usefulness in practical applications, the proposed distribution and the associated Ąrst-order autoregressive process are compared to other competing distributions and processes, using to this end several real data sets. In the context of statistical quality control, Ąnally a cumulative sum control chart is developed for monitoring the process mean. To illustrate its usefulness, both simulation and real data analysis are performed.

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Section: Introductionmentioning

confidence: 99%

The discrete new XLindley distribution and the associated autoregressive process

Maya,

Jodrá,

Aswathy

et al. 2024

Int J Data Sci Anal

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“…Basically, there is an ongoing vast literature on the handling of the overdispersion in the simple INAR process (Weiß 2008 ; Awale et al. 2021 ; Huang and Zhu 2021 ; Weiß 2020 ). However, we note that the construction of the INAR process, in addition to the self-decomposability properties, becomes simpler with assuming the distribution of the innovation series, and without compromising on the marginal distribution of the counting series (See Bourguignon et al.…”

Section: Introductionmentioning

confidence: 99%

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

Mohammadi

Sajjadnia

Sharafi

et al. 2022

Iran J Sci Technol Trans Sci

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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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“…Recently, to cover some unique properties of real data sets, other distributions were designated for innovation of the IANR(1) models, such as power series (Bourguignon and Vasconcellos 2015 ), Poisson-transmuted exponential (Altun and Mamode Khan 2021 ) and Bell (Huang and Zhu 2021 ).…”

Section: Introductionmentioning

confidence: 99%

An INAR(1) Time Series Model via a Modified Discrete Burr–Hatke with Medical Applications

Shirozhan¹,

Khan

Bakouch

2022

Iran J Sci

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This paper introduces a flexible discrete transmuted record type discrete Burr–Hatke (TRT-DBH) model that seems suitable for handling over-dispersion and equi-dispersion in count data analysis. Further to the elegant properties of the TRT-DBH, we propose, in the time series context, a first-order integer-valued autoregressive process with TRT-DBH distributed innovations [TRBH-INAR(1)]. The moment properties and inferential procedures of this new INAR(1) process are studied. Some Monte Carlo simulation experiments are executed to assess the consistency of the parameters of the TRBH-INAR(1) model. To further motivate its purpose, the TRBH-INAR(1) is applied to analyze the series of the COVID-19 deaths in Netherlands and the series of infected cases due to the Tularaemia disease in Bavaria. The proposed TRBH-INAR(1) model yields superior fitting criteria than other established competitive INAR(1) models in the literature. Further diagnostics related to the residual analysis and forecasting based on the TRBH-INAR(1) model are also discussed. Based on modified Sieve bootstrap predictors, we provide integer forecasts of future death of COVID-19 and infected of Tularemia.

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A New First-Order Integer-Valued Autoregressive Model with Bell Innovations

Cited by 19 publications

References 31 publications

The discrete new XLindley distribution and the associated autoregressive process

The discrete new XLindley distribution and the associated autoregressive process

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

An INAR(1) Time Series Model via a Modified Discrete Burr–Hatke with Medical Applications

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