A bivariate Sarmanov regression model for count data with generalised Poisson marginals

Hofer, Vera; Leitner, Johannes

doi:10.1080/02664763.2012.724661

Cited by 13 publications

(9 citation statements)

References 31 publications

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“…Lee () highlighted the Sarmanov family of distributions (Sarmanov, ), which have seen a resurgence in interest (Hofer & Leitner, ; Pelican & Vernic, ; Lin et al ., ). For the white mould data, a Sarmanov bivariate distribution with NB marginals was derived, and the fitted parameter ω satisfied the required boundary constraints.…”

Section: Discussionmentioning

confidence: 99%

Probability distributions for marketable pods and white mould on snap bean

Shah

Dillard

Pethybridge

2017

Annals of Applied Biology

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White mould, caused by Sclerotinia sclerotiorum, is one of the most recalcitrant diseases of snap bean. Probability distributions suitable for describing the total number of marketable pods (hereafter simply referred to as pods) per plant, as well as for the number of pods and stems with white mould per plant, have not been identified. The total number of pods and the number of pods and stems with white mould were measured on a per plant basis in plots of processing snap bean (var. Hystyle) in New York. The total number of pods per plant ranged from 0 to 29, and was best described by the Pólya-Aeppli distribution. The number of pods and the number of stems with white mould per plant were well-described by the negative binomial (NB) distribution. A Sarmanov bivariate distribution with NB marginals was derived and fitted to the joint data on the number of pods and stems with white mould per plant, accounting for correlation between pods and stems with white mould on the same plant. The bivariate distribution was used to formulate an empirical equation for the incidence of plants with white mould as a function of the average number of pods and stems with white mould per plant. The results represented a more complete understanding of the distributional properties of white mould in snap bean.

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Section: Discussionmentioning

confidence: 99%

Probability distributions for marketable pods and white mould on snap bean

Shah

Dillard

Pethybridge

2017

Annals of Applied Biology

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“…For instance, the correct range can be found in section 2.2 (after eq. ( 1)) from Hofer and Leitner (2012); see also Lee (1996). Using that result in the particular case given in ( 5), we obtain that…”

Section: Existing Bivariate Ingarch Models and Their Limitationsmentioning

confidence: 94%

Flexible bivariate INGARCH process with a broad range of contemporaneous correlation

Barreto‐Souza

Ombao

2022

Journal Time Series Analysis

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We propose a novel flexible bivariate conditional Poisson (BCP) INteger-valued Generalized AutoRegressive Conditional Heteroscedastic (INGARCH) model for correlated count time series data. Our proposed BCP-INGARCH model is mathematically tractable and has as the main advantage over existing bivariate INGARCH models its ability to capture a broad range (both negative and positive) of contemporaneous cross-correlation, which is a non-trivial advancement. Properties of stationarity and ergodicity for the BCP-INGARCH process are developed. Estimation of the parameters is performed through conditional maximum likelihood (CML), and the finite-sample behavior of the estimators is investigated through simulation studies. Asymptotic properties of the CML estimators are derived. Hypothesis testing methods for the presence of contemporaneous correlation between the time series are presented and evaluated. A Granger causality test is also addressed. We apply our methodology to monthly counts of hepatitis cases in two nearby Brazilian cities, which are highly cross-correlated. The data analysis demonstrates the importance of considering a bivariate model allowing for a wide range of contemporaneous correlation in real-life applications.

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“…For instance, the correct range can be found in Subsection 2.2 (after Eq. ( 1)) from Hofer and Leitner (2012); see also Lee (1996). Using that result in the particular case given in ( 9), we obtain that…”

Section: Existing Bivariate Ingarch Models and Their Limitationsmentioning

confidence: 94%

Flexible Bivariate INGARCH Process With a Broad Range of Contemporaneous Correlation

C.¹,

Barreto‐Souza²,

Ombao³

2020

Preprint

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We propose a novel flexible bivariate conditional Poisson (BCP) INteger-valued Generalized AutoRegressive Conditional Heteroscedastic (INGARCH) model for correlated count time series data. Our proposed BCP-INGARCH model is mathematically tractable and has as the main advantage over existing bivariate INGARCH models its ability to capture a broad range (both negative and positive) of contemporaneous cross-correlation which is a non-trivial advancement. Properties of stationarity and ergodicity for the BCP-INGARCH process are developed. Estimation of the parameters is performed through conditional maximum likelihood (CML) and finite sample behavior of the estimators are investigated through simulation studies. Asymptotic properties of the CML estimators are derived. Additional simulation studies compare and contrast methods of obtaining standard errors of the parameter estimates, where a bootstrap option is demonstrated to be advantageous. Hypothesis testing methods for the presence of contemporaneous correlation between the time series are presented and evaluated.We apply our methodology to monthly counts of hepatitis cases at two nearby Brazilian cities,

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A bivariate Sarmanov regression model for count data with generalised Poisson marginals

Cited by 13 publications

References 31 publications

Probability distributions for marketable pods and white mould on snap bean

Probability distributions for marketable pods and white mould on snap bean

Flexible bivariate INGARCH process with a broad range of contemporaneous correlation

Flexible Bivariate INGARCH Process With a Broad Range of Contemporaneous Correlation

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