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ON THE UNIMODALITY OF THE GENERALIZED NEGATIVE BINOMIAL DISTRIBUTION
Statistica Neerlandica, 1986Abstract.It is shown that the generalized negative binomial distribution which is useful in random walks, queueing theory and branching processes is unimodal. When nθ(1 –θ)β‐1 > 1, the mode is not at the pointx= 0 and for that case, the lower and the upper bounds of the mode are obtained.
Consul, P. C., Famoye, F.
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A new generalization of the negative binomial distribution
Computational Statistics & Data Analysis, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ramesh C. Gupta, S. H. Ong 0002
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On the generalized negative binomial distribution
Communications in Statistics - Theory and Methods, 1995The generalized negative binomial distribution (GNBD) was defined and studied by Jain and Consul (1971). The GNBD model has been found useful in many fields such as random walk, queuing theory, branching processes and polymerization reaction in chemistry. In this paper, four methods by which the GNBD model gets generated are discussed.
P. C. Consul, Felix Famoye
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Bayesian Estimation in a Generalized Negative Binomial Distribution
Biometrical Journal, 1986AbstractA generalized negative binomial (GNB) distribution was introduced by JAIN and CONSUL (1971) and was modified by NELSON (1975). The probability function of the distribution is defined by the function p(x; m, β, θ)= θx (1 ‐ θ)m+βx—x for x=0, 1, …, and zero otherwise, where m>0, 0<θ<1 and β=0 or 1≦β<θ−1.
Islam, M. N., Consul, P. C.
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A Bivariate Generalization of the Noncentral Negative Binomial Distribution
Communications in Statistics - Simulation and Computation, 2013This article proposes a bivariate generalization of the noncentral negative binomial distribution which arises as a model in photon and neural counting. This bivariate generalization is derived as a mixed shifted bivariate negative binomial distribution.
Seng Huat Ong, Choung Min Ng
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On a generalization of class of negative binomial distributions
Discrete Mathematics and Applications, 2022Abstract A class of one-dimensional discrete power series distributions containing negative binomial distributions is considered. Properties of distributions of this class are investigated. Limit theorems generalizing similar theorems for the negative binomial distributions are proved.
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On the negative binomial distribution and its generalizations
Statistics & Probability Letters, 2007Some representations of the negative binomial distribution \(NB(r,p)\) are given. Specifically, it was proved that \(NB(r,p)\) may be represented, under suitable assumptions, as the distribution of: (a) the sum of dependendent geometric random variables; (b) the number of trials for the r-th success, based on a sequence of dependent Bernoulli random ...
VELLAISAMY, P, UPADHYE, NS
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Generalized Negative Binomial Distributions
Journal of Statistical Physics, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized distribution of negative binomial states
SPIE Proceedings, 1992We present analytical expression for the s-parametrized quasiprobability distribution W((alpha) , (epsilon) , s) for the negative binomial states. As special cases, for s equals -1, 0, and 1, W((alpha) , (epsilon) , s) reduces to the Q-distribution, the Wigner distribution, and the Glauber-Sudarshan P-function, respectively.
Richard D'Souza, Adya P. Mishra
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