Bivariate Zero-Inflated Power Series Distribution

Krishna, Patil Maruti; Tukaram, Shirke Digambar

doi:10.4236/am.2011.27110

“…where (0,θ H0 ) denote the constrained MLEs of (ϕ, θ) under H 0 and (φ,θ) denote the unconstrained MLEs of (ϕ, θ), which are obtained by the algorithm specified in (11)- (12). Since the null hypothesis in (19) corresponds to ϕ being on the boundary of the parameter space and the appropriate null distribution is a 50:50 mixture of χ 2 (0) (i.e., the degenerate distribution with all mass at zero) and χ 2 (1), see Self & Liang [25] and Feng & McCulloch [14]. Hence, the p-value ([16], p.78; [17], p.225) is…”

Section: Se(θ)mentioning

confidence: 99%

“…In this subsection, we investigate the performance of the LRT for testing hypotheses (19) and (22) for the Type I bivariate ZIGP λ distribution. We conduct extensive simulations to observe the changes of type I error rates and powers against the sample sizes which are set to be n = 500(50)950.…”

Section: Performance Of the Lrt In Type I Bivariate Zigp λmentioning

confidence: 99%

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

Zhang

¹

,

Tian

²

,

Huang

³

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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“…Since the null hypothesis in (19) corresponds to ϕ being on the boundary of the parameter space and the appropriate null distribution is a 50:50 mixture of χ 2 (0) (i.e., the degenerate distribution with all mass at zero) and χ 2 (1), see Self & Liang [25] and Feng & McCulloch [14]. Hence, the p-value ([16], p.78; [17], p.225) is…”

Section: Likelihood Ratio Test For Zero Inflation Suppose We Want Tomentioning

confidence: 99%

“…In this subsection, we investigate the performance of the LRT for testing hypotheses (19) and (22) for the Type I bivariate ZIGP λ distribution. We conduct extensive simulations to observe the changes of type I error rates and powers against the sample sizes which are set to be n = 500(50)950.…”

Section: Performance Of the Lrt In Type I Bivariate Zigp λmentioning

confidence: 99%

“…Their models can only fit over-dispersed data with positive correlation. Krishna & Tukaram [19] provided a bivariate power series distribution that utilized the multiplicative factor form and incorporated inflation at zero. Bivariate zero-inflated Poisson distribution were then discussed as a special case of power series distributions and the associated properties were explored.…”

Section: Tablementioning

confidence: 99%

See 1 more Smart Citation

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

Zhang

¹

,

Tian

²

,

Huang

³

2015

Stat., optim. inf. comput.

View full text Add to dashboard Cite

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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Flexible multivariate zero to k inflated power series regression model with applications

Saboori

¹

,

Doostparast

²

2022

Stat

1

0

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Inflated distributions are applied in various fields, including insurance, traffic networks and survival analyses. First, they are defined by a baseline discrete distribution, and then, extra masses are added to some points of interest, called inflated points, to achieve more flexible models for data analyses. The baseline distribution is arbitrary and application dependent. Here, the rich family of power series distributions is considered as the baseline, which includes various common discrete distributions such as Poisson, negative binomial, multinomial and logarithmic series distributions. This paper deals with an extension of previous works in two directions. The former is an extension of the univariate inflated distributions to multivariate ones, and the latter is the generalization of the inflated points from the zero single point to the set k=0,1,…. Under this setting, various inflated distributions in the literature fall into the proposed family of distributions. These extensions make the proposed model flexible and practically useful in data analyses. To do this, the problem of estimating parameters with various approaches as well as hypotheses testing is studied in detail. Multivariate‐generalized linear models with inflated multivariate discrete responses are also discussed. To assess the performance of the proposed family of inflated distributions, simulation studies are conducted, and a real data set on an Australian health survey study is also analysed.

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Bivariate Zero-Inflated Power Series Distribution

Cited by 9 publications

References 10 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

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

Flexible multivariate zero to k inflated power series regression model with applications

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