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Statistics and Probability Letters, 1992
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Kunio Tanabe
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Kunio Tanabe
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Which negative multinomial distributions are infinitely divisible?
Bernoulli, 2003 A general class of negative multinomial distributions on \(\mathbb N_0^n\) is defined by its probability generating functions to be of the form \((A(a_1,\dots,a_n)/A(a_1z_1,\dots,a_nz_n))^\lambda\) for some \(\lambda>0\) and some function \( A(\mathbf z)=\sum_{T\subset\{1,\dots,n\}}a_T\prod_{i\in T}z_i\).
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A characterization of multinomial and negative multinomial distributions
Scandinavian Actuarial Journal, 1974Abstract The intent of this paper is to show that the independent random vectors x and y have multinomial (negative mUltinomial) distributions with the same parameter vector o, and the other parameters being respectively m and n if and only if the conditional distribution of x given x + y is multivariate hypergeometric (multivariate inverse ...
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Domain of existence of the Laplace transform of negative multinomial distributions and simulations
Statistics & Probability Letters, 2023A probability distribution \( \sum_{\boldsymbol{\alpha} \in \mathbb{N}^n} p_{\boldsymbol{\alpha}}\delta_{\boldsymbol{\alpha}}\) on the set of nonnegative integers \(\mathbb{N}^n\) is said to be a negative multinomial distribution if there exists an affine polynomial \(P(z_1,\dots , z_n)\) and \(\lambda >0\) such that \[ \sum_{\boldsymbol{\alpha} \in ...
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Conditionally negative association resulting from multinomial distribution
Statistics & Probability Letters, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuan, Demei, Zheng, Jianhua
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Communications in Statistics - Theory and Methods, 1996
Lenk, Rao and Tibrewala (1993) have introduced a Negative Multinomial Distribution derived from a nonstationary Poisson process with intensity function , which incorporates marketing mix variables. It is shown that under certain conditions, the maximum likelihood estimates of the parameters of the proposed model do not exist.
J.K. Ghorai, Sanjoy Ghose
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Lenk, Rao and Tibrewala (1993) have introduced a Negative Multinomial Distribution derived from a nonstationary Poisson process with intensity function , which incorporates marketing mix variables. It is shown that under certain conditions, the maximum likelihood estimates of the parameters of the proposed model do not exist.
J.K. Ghorai, Sanjoy Ghose
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Integral expressions for tail probabilities of the negative multinomial distribution
Annals of the Institute of Statistical Mathematics, 1975An alternative simple derivation is given for some integral expressions for tail probabilities of the negative multinomial distribution obtained by Olkin & Sobel [3] inBiometrika. The new derivation is based on the fact that the negative multinomial distribution is a certain mixture of the multiple Poisson distribution and on a well known integral ...
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Biometrika, 1963
INTRODUCTION In the generalization of Bernoulli trials where we have k possible outcomes of each trial, k let the probability of the ith outcome in each trial be pi (i = 1,...,k) where Pi= 1. i=l For a fixed number of trials (n), the probability of exactly x1 occurrences of outcome 1, x2 of 2, ..., Xk of k is given by the multinomial distribution.
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INTRODUCTION In the generalization of Bernoulli trials where we have k possible outcomes of each trial, k let the probability of the ith outcome in each trial be pi (i = 1,...,k) where Pi= 1. i=l For a fixed number of trials (n), the probability of exactly x1 occurrences of outcome 1, x2 of 2, ..., Xk of k is given by the multinomial distribution.
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2019
Clinical trials that compare one or more experimental treatments to a control treatment in which event incidence (i.e. incidence of disease or an adverse event) is rare often assume that comparative Poisson methodology is appropriate for modeling the number of events that occur in each treatment group.
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Clinical trials that compare one or more experimental treatments to a control treatment in which event incidence (i.e. incidence of disease or an adverse event) is rare often assume that comparative Poisson methodology is appropriate for modeling the number of events that occur in each treatment group.
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Mixtures, compounds and inflations of negative multinomial distribution
The paper considers some relations between mixed, compound and inflated geometric and negative multinomial distributions. The dependence structure of multivariate random sums (compounds), discussed in this paper, is born to two factors, the equal number of summands in the coordinates and the multivariate distribution of the coordinates with equal ...openaire +1 more source