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Generalized Negative Binomial Distributions

Journal of Statistical Physics, 2000
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A Generalized Negative Binomial Distribution

SIAM Journal on Applied Mathematics, 1971
A generalized negative binomial (GNB) distribution with an additional parameter $\beta $ has been obtained by using Lagrange’s expansion. The parameter is such that both mean and variance tend to increase or decrease with an increase or decrease in its value but the variance increases or decreases faster than the mean.
Jain, G. C., Consul, P. C.
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The Hyper‐Negative Binomial Distribution

Biometrical Journal, 1987
AbstractA generalized family of the negative binomial distribution is introduced in a paper by Srivastava, Yousry and Ahmed (1986). It is a solution of the difference equation equation image and is called the hyper‐negative binomial distribution. Certain properties including the moments of the distribution are presented.
Yousry, M. A., Srivastava, R. C.
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THE TRUNCATED NEGATIVE BINOMIAL DISTRIBUTION

Biometrika, 1955
(1920), Fisher (1941), Haldane (1941), Anscoinbe (1950) and Bliss & Fisher (1953), and is extensively used for the description of data too heterogeneous to be fitted by a Poisson distribution. Observed samples, however, may be truncated, in the sense that the number of individuals falling into the zero class cannot be determined.
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The Negative Binomial Distribution

The Statistician, 1985
This note sketches a biological context for the negative binomial distribu- tion, gives some of the many equivalent mathematical notations that have been used for the negative binomial probabilities, and discusses the use of the computer program MLP (the Maximum Likelihood Program) for fitting negative binomial distributions to data.
G. J. S. Ross, D. A. Preece
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The Non‐Central Negative Binomial Distribution

Biometrical Journal, 1979
AbstractThe non‐central negative binomial distribution is derived by mixing the POISSONdistribution with a certain BESSELfunction distribution, or the negative binomial distribution with the POISSONdistribution. Some properties of the distribution are discussed, including a characterization.
Ong, S. H., Lee, P. A.
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Quasiprobability distributions of negative binomial states

Physical Review A, 1992
We present the s-parametrized quasiprobability distributions for the negative binomial states. Marked changes in the quasiprobability distributions W(α,e,s) are exhibited by states that are close to the random-phase coherent state (e=0), as the parameter s is varied continuously from s=-1, corresponding to the Q function, to s=1, corresponding to the P
, D'Souza, , Mishra
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Fitting the Negative Binomial Distribution

Biometrics, 1986
This note is a reaction to recent papers in this journal by Willson, Folks, and Young (1984) and Bowman (1984). For the biometrical analysis of certain kinds of observations, such as insect counts, accident counts, or cave entrance counts, when only nonnegative integers are observable, it is expedient to restrict attention to those random variables ...
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Truncated Binomial and Negative Binomial Distributions

Journal of the American Statistical Association, 1955
(1955). Truncated Binomial and Negative Binomial Distributions. Journal of the American Statistical Association: Vol. 50, No. 271, pp. 877-883.
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The Negative Binomial Distribution

1989
We begin with a new problem: a blood bank continues to purchase blood from individuals until it collects 6 pints of type B negative needed for an upcoming operation. How many pints should they be prepared to buy?
Hung T. Nguyen, Gerald S. Rogers
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