Negative multinomial distribution

Sibuya, Masaaki; Yoshimura, Isao; Shimizu, Ryoichi

doi:10.1007/bf02868583

Cited by 79 publications

(32 citation statements)

References 13 publications

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“…However, if the loss function is L, (8,8), the special case of (3.1) (or (1.1)) with K(.) --I, it can be shown by using the difference inequality method that 8~ is dominated by a class of estimators even for n.=l.…”

Section: Multivariate Negative Multinomial Casementioning

confidence: 98%

“…For the special case K(.) --l, denote the corresponding risk function as R, (8,5). The notation is used throughout this paper.…”

Section: Lemma 2 Let Z Be a Random Variable Suppose Hi() And H~()mentioning

confidence: 99%

“…Sibuya, Yoshimura and Shimizu [8] provide a comprehensive review of the properties of the negative multinomial distribution. In particular, many situations where such a distribution arises are described.…”

Section: Introductionmentioning

confidence: 99%

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Multiparameter estimation for some multivariate discrete distributions with possibly dependent components

Tsui

1986

Ann Inst Stat Math

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SummaryIn multiparameter estimation for multivariate discrete distributions with infinite support, inadmissibility problems in situations where the multivariate probability distribution function is not a product of the one-dimensional marginal probability distribution functions have previously been unexplored. This paper examines the inadmissibility problem in some of these situations. Special attention is given to estimating the mean of a negative multinomial distribution. In estimating the mean vector, certain Clevenson-Zidek type estimators are shown to be uniformly better than the usual estimator under a large class of generally scaled squared loss functions. Some of the results are generalized to other multivariate discrete distributions and to situations where several independent negative multinomial distributions are considered.

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Section: Multivariate Negative Multinomial Casementioning

confidence: 98%

“…For the special case K(.) --l, denote the corresponding risk function as R, (8,5). The notation is used throughout this paper.…”

Section: Lemma 2 Let Z Be a Random Variable Suppose Hi() And H~()mentioning

confidence: 99%

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Multiparameter estimation for some multivariate discrete distributions with possibly dependent components

Tsui

1986

Ann Inst Stat Math

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“…, F J |N ) may suggest this point more clearly. Sibuya et al (1964) noted that the conditional model of the gamma-Poisson mixture (=negative binomial distribution) given N equals the Dirichlet-multinomial mixture or multivariate negative hypergeometric distributions. Hoshino (2002a) investigates parallel relationships of the CIGP distribution to those of the Dirichlet-multinomial mixture, based on Hoshino and Takemura (1998)'s discussion.…”

Section: On the Property Of The Cigp Distributionmentioning

confidence: 99%

Random Clustering Based on the Conditional Inverse Gaussian-Poisson Distribution

Hoshino

2003

JJSS

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The present article describes a Conditional Inverse Gaussian-Poisson (CIGP) distribution, obtained by conditioning an inverse Gaussian-Poisson population model on its total frequency. This CIGP distribution is equivalent to random partitioning of positive integers, with the possibility for a number of applications in statistical ecology, linguistics and statistical disclosure control to name a few. After showing the marginal moments of the distribution, parameter estimation is discussed. Fitting the CIGP distribution to some typical data sets demonstrates its applicability.

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“…In connection with the negative multinomial distribution, Sibuya, Yoshimura, and Shimizu [5] discuss a slight modification of the Eggenberger Polya Urn Scheme and obtain a multivariate distribution which tends to the negative multinomial under certain limiting conditions.…”

Section: Introductionmentioning

confidence: 98%

On multivariate modified Polya and inverse Polya distributions and their properties

Janardan

Patil

1974

Ann Inst Stat Math

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Negative multinomial distribution

Cited by 79 publications

References 13 publications

Multiparameter estimation for some multivariate discrete distributions with possibly dependent components

Multiparameter estimation for some multivariate discrete distributions with possibly dependent components

Random Clustering Based on the Conditional Inverse Gaussian-Poisson Distribution

On multivariate modified Polya and inverse Polya distributions and their properties

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