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On the Normal Approximation to the Hypergeometric Distribution [PDF]
The Annals of Mathematical Statistics, 1956 In this paper a new normal approximation to a sum of hypergeometric terms is derived, which is a direct generalization of Feller's normal approximation to the binomial distribution [2]. For intervals that are asymmetric with respect to the mean, or when the distribution is skewed, the new approximation is a marked improvement over the classical ...
W. L. Nicholson
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MethodsX, 2021 In probability theory and statistics, the probability distribution of the sum of two or more independent and identically distributed (i.i.d.) random variables is the convolution of their individual distributions.
Arne Johannssen +2 more
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The maximum negative hypergeometric distribution [PDF]
arXiv: Statistics Theory, 2005 An urn contains a known number of balls of two different colors. We describe the random variable counting the smallest number of draws needed in order to observe at least $\,c\,$ of both colors when sampling without replacement for a pre-specified value of $\,c=1,2,\ldots\,$.
Daniel Zelterman
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Random continued fractions with beta-hypergeometric distribution
The Annals of Probability, 2012 28 pages, 11 figures.
Gérard Letac, PICCIONI, MAURO
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Distributional solutions of the hypergeometric differential equation
Journal of Mathematical Analysis and Applications, 1987 AbstractWe present the distributional solutions to the hypergeometric differential equation. These solutions are obtained in the form of infinite series of the Dirac Delta functions and its derivatives. We employ these solutions to observe their interesting features.
Ram P. Kanwal, Lance L. Littlejohn
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Properties of the Extended Hypergeometric Distribution [PDF]
The Annals of Mathematical Statistics, 1965 W. L. Harkness
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The tail of the hypergeometric distribution
Discrete Mathematics, 1979 Vašek Chvátal
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Multivariate Generalization of the Gauss Hypergeometric Distribution [PDF]
Hacettepe Journal of Mathematics and Statistics, 2014 The Gauss hypergeometric distribution with the density proportional to x 1 (1 x) 1 (1 +x ) , 0 < x < 1 arises in connection with the prior distribution of the parameter (0 < < 1) representing trac intensity in aM=M=1 queue system. In this article, we define and study a multivariate generalization of this distribution and derive some of its properties ...
Nagar, Daya Krishna +2 more
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Interchanging Parameters of the Hypergeometric Distribution [PDF]
Mathematics Magazine, 1993 Bruce R. Johnson, R. R. Davidson
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Hahn polynomials for hypergeometric distribution
Advances in Applied Mathematics, 2022 Orthogonal polynomials for the multivariate hypergeometric distribution are defined on lattices in polyhedral domains in $\RR^d$. Their structures are studied through a detailed analysis of classical Hahn polynomials with negative integer parameters. Factorization of the Hahn polynomials is explored and used to explain the relation between the index ...
Iliev, Plamen, Xu, Yuan
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