Type I multivariate zero-inflated Poisson distribution with applications

Liu, Yin; Tian, Guo‐Liang

doi:10.1016/j.csda.2014.10.010

Cited by 31 publications

(39 citation statements)

References 26 publications

(32 reference statements)

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“…Besides, since both marginal count data are over-dispersed according to their marginal sample means and variances, the bivariate Poisson distribution constructed by the trivariate reduction method is also not appropriate due to the property of equi-dispersion. Note that the over-dispersion may result from the excess (0,0) points in the observations, the Type I multivariate ZIP distribution proposed by Liu & Tian [22] could be considered. If we fit the data by the Type I bivariate ZIP distribution, denoted by …”

Section: Marginal Analysismentioning

confidence: 99%

“…, which is a special case of the Type I multivariate ZIP distribution recently developed by Liu & Tian [22].…”

Section: Type I Bivariate Zero-inflated Generalized Poisson Distributmentioning

confidence: 99%

“…For example, there are seven zero values of Y out of a total of 12 observations in Table 1. The multivariate zero-inflated Poisson models were developed by using the mixture technique [21] and by using the stochastic representation technique [22]. Their models can only fit over-dispersed data with positive correlation.…”

Section: Tablementioning

confidence: 99%

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Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Zhang

Tian

Huang

2015

Stat., optim. inf. comput.

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To model correlated bivariate count data with extra zero observations, this paper proposes two new bivariate zero-inflated generalized Poisson (ZIGP) distributions by incorporating a multiplicative factor (or dependency parameter) λ, named as Type I and Type II bivariate ZIGP λ distributions, respectively. The proposed distributions possess a flexible correlation structure and can be used to fit either positively or negatively correlated and either over-or under-dispersed count data, comparing to the existing models that can only fit positively correlated count data with over-dispersion. The two marginal distributions of Type I bivariate ZIGP λ share a common parameter of zero inflation while the two marginal distributions of Type II bivariate ZIGP λ have their own parameters of zero inflation, resulting in a much wider range of applications. The important distributional properties are explored and some useful statistical inference methods including maximum likelihood estimations of parameters, standard errors estimation, bootstrap confidence intervals and related testing hypotheses are developed for the two distributions. A real data are thoroughly analyzed by using the proposed distributions and statistical methods. Several simulation studies are conducted to evaluate the performance of the proposed methods.

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Section: Marginal Analysismentioning

confidence: 99%

“…, which is a special case of the Type I multivariate ZIP distribution recently developed by Liu & Tian [22].…”

Section: Type I Bivariate Zero-inflated Generalized Poisson Distributmentioning

confidence: 99%

See 1 more Smart Citation

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Zhang

Tian

Huang

2015

Stat., optim. inf. comput.

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“…Extra zeros are common features of count data in many disciplines including epidemiology, public health, biology, sociology, psychology, engineering, agriculture and especially for ecological data sets [1]. The characteristic of ecological data consists of measuring binary presence or absence, counts of abundance, proportional occupancy rates, or continuous population densities which have high tendency to contain many zero values [2].…”

Section: Introductionmentioning

confidence: 99%

Analysing count data of Butterflies communities in Jasin, Melaka: A Poisson regression analysis

Jamil

Abdullah

Kek

et al. 2017

J. Phys.: Conf. Ser.

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Abstract. Counting outcomes normally have remaining values highly skewed toward the right as they are often characterized by large values of zeros. The data of butterfly communities, had been taken from Jasin, Melaka and consists of 131 number of subject visits in Jasin, Melaka. In this paper, considering the count data of butterfly communities, an analysis is considered Poisson regression analysis as it is assumed to be an alternative way on better suited to the counting process. This research paper is about analysing count data from zero observation ecological inference of butterfly communities in Jasin, Melaka by using Poisson regression analysis. The software for Poisson regression is readily available and it is becoming more widely used in many field of research and the data was analysed by using SAS software. The purpose of analysis comprised the framework of identifying the concerns. Besides, by using Poisson regression analysis, the study determines the fitness of data for accessing the reliability on using the count data. The finding indicates that the highest and lowest number of subject comes from the third family (Nymphalidae) family and fifth (Hesperidae) family and the Poisson distribution seems to fit the zero values.

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“…Zero-inflated Poisson (ZIP) regression [2][3] and zeroinflated negative binomial (ZINB) regression are suitable for modelling the count data. There are four scenarios of zero occurrences in ecological data and the modelling approach recommended for presence or absence and for count data, where zero inflation can be caused by false zeros, true zeros or a combination of both.…”

Section: Introductionmentioning

confidence: 99%

Detecting overdispersion in count data: A zero-inflated Poisson regression analysis

Jamil

Abdullah

Kek

et al. 2017

J. Phys.: Conf. Ser.

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Abstract. This study focusing on analysing count data of butterflies communities in Jasin, Melaka. In analysing count dependent variable, the Poisson regression model has been known as a benchmark model for regression analysis. Continuing from the previous literature that used Poisson regression analysis, this study comprising the used of zero-inflated Poisson (ZIP) regression analysis to gain acute precision on analysing the count data of butterfly communities in Jasin, Melaka. On the other hands, Poisson regression should be abandoned in the favour of count data models, which are capable of taking into account the extra zeros explicitly. By far, one of the most popular models include ZIP regression model. The data of butterfly communities which had been called as the number of subjects in this study had been taken in Jasin, Melaka and consisted of 131 number of subjects visits Jasin, Melaka. Since the researchers are considering the number of subjects, this data set consists of five families of butterfly and represent the five variables involve in the analysis which are the types of subjects. Besides, the analysis of ZIP used the SAS procedure of overdispersion in analysing zeros value and the main purpose of continuing the previous study is to compare which models would be better than when exists zero values for the observation of the count data. The analysis used AIC, BIC and Voung test of 5% level significance in order to achieve the objectives. The finding indicates that there is a presence of over-dispersion in analysing zero value. The ZIP regression model is better than Poisson regression model when zero values exist.

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Type I multivariate zero-inflated Poisson distribution with applications

Cited by 31 publications

References 26 publications

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Analysing count data of Butterflies communities in Jasin, Melaka: A Poisson regression analysis

Detecting overdispersion in count data: A zero-inflated Poisson regression analysis

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