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Discrete probability distribution
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k {\displaystyle
Hypergeometric_distribution
Discrete probability distribution
In probability theory and statistics, the negative hypergeometric distribution describes probabilities for when sampling from a finite population without
Negative hypergeometric distribution
Negative_hypergeometric_distribution
and statistics, Fisher's noncentral hypergeometric distribution is a generalization of the hypergeometric distribution where sampling probabilities are modified
Fisher's noncentral hypergeometric distribution
Fisher's_noncentral_hypergeometric_distribution
Wallenius' noncentral hypergeometric distribution (named after Kenneth Ted Wallenius) is a generalization of the hypergeometric distribution where items are
Wallenius' noncentral hypergeometric distribution
Wallenius'_noncentral_hypergeometric_distribution
Expectation or average of the falling factorial of a random variable
understood to be zero if r > n. If a random variable X has a hypergeometric distribution with population size N, number of success states K ∈ {0,...,N}
Factorial_moment
Mathematical function for the probability a given outcome occurs in an experiment
univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. A commonly encountered
Probability_distribution
Discrete probability distribution
known as the negative hypergeometric distribution. The beta distribution is a conjugate distribution of the binomial distribution. This fact leads to an
Beta-binomial_distribution
Probability distribution
resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution remains a good
Binomial_distribution
Hypergeometric distribution
In statistics, the hypergeometric distribution is the discrete probability distribution generated by picking colored balls at random from an urn without
Noncentral hypergeometric distributions
Noncentral_hypergeometric_distributions
casino roulette, or the first card of a well-shuffled deck. The hypergeometric distribution, which describes the number of successes in the first m of a
List of probability distributions
List_of_probability_distributions
Function defined by a hypergeometric series
the Gaussian or ordinary hypergeometric function 2F1(a, b; c; z) is a special function represented by the hypergeometric series, that includes many
Hypergeometric_function
Topics referred to by the same term
Hypergeometric may refer to several distinct concepts within mathematics: The hypergeometric function, a solution to the Gaussian hypergeometric differential
Hypergeometric
Game of chance
that are picked on each ticket. Keno probabilities come from a hypergeometric distribution. For Keno, one calculates the probability of hitting exactly
Keno
Probability distribution
spreading COVID-19. Hypergeometric distribution Coupon collector's problem Compound Poisson distribution Negative binomial distribution Johnson, Norman L
Geometric_distribution
Statistical significance test
Fisher, this leads under a null hypothesis of independence to a hypergeometric distribution of the numbers in the cells of the table. This setting is however
Fisher's_exact_test
Type of probability distribution
multinomial distribution, the negative multinomial distribution, the multivariate hypergeometric distribution, and the elliptical distribution. Bayesian
Joint probability distribution
Joint_probability_distribution
British polymath (1890–1962)
the parameter". Fisher's noncentral hypergeometric distribution, a generalization of the hypergeometric distribution, where sampling probabilities are modified
Ronald_Fisher
Mental exercise in probability and statistics
draws before the first successful (correctly colored) draw. hypergeometric distribution: the balls are not returned to the urn once extracted. Hence
Urn_problem
Continuous probability distribution
exponential distribution is the continuous analogue of the geometric distribution, the hyperexponential distribution is not analogous to the hypergeometric distribution
Hyperexponential_distribution
Generalization of the binomial distribution
without replacement, so the correct distribution is the multivariate hypergeometric distribution, but the distributions converge as the population grows
Multinomial_distribution
Discrete probability distribution
"Moment Recurrence Relations for Binomial, Poisson and Hypergeometric Frequency Distributions" (PDF). Annals of Mathematical Statistics. 8 (2): 103–111
Poisson_distribution
Exact test
the data come from double-binomial distribution, the conditioning (that leads to using the hypergeometric distribution for calculating the Fisher's exact
Barnard's_test
Probability distribution
theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable
Normal_distribution
Continuous probability distribution
{\displaystyle U(a,b,z)} is the confluent hypergeometric function of the second kind. In instances where the F-distribution is used, for example in the analysis
F-distribution
Statistical confidence interval for success counts
repeated draws of a binomial distribution. In this case, the underlying distribution would be the hypergeometric distribution. The interval boundaries can
Binomial proportion confidence interval
Binomial_proportion_confidence_interval
Probability distribution in physics
probability density function is expressed in terms of hypergeometric functions. The Holtsmark distribution has applications in plasma physics and astrophysics
Holtsmark_distribution
Number of subsets of a given size
{\displaystyle \alpha } . Binomial transform Delannoy number Eulerian number Hypergeometric function List of factorial and binomial topics Macaulay representation
Binomial_coefficient
Famous randomized experiment
Thus the number of successes is distributed according to the hypergeometric distribution. Specifically, for a random variable X {\displaystyle X} equal
Lady_tasting_tea
Mathematical theorem on convolved binomial coefficients
probabilities. The resulting probability distribution is the hypergeometric distribution. That is the probability distribution of the number of red marbles in
Vandermonde's_identity
Solution of a confluent hypergeometric equation
a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential
Confluent hypergeometric function
Confluent_hypergeometric_function
Probability distribution
Negative Binomial Distribution". Wroughton, Jacqueline. "Distinguishing Between Binomial, Hypergeometric and Negative Binomial Distributions" (PDF). Hilbe
Negative binomial distribution
Negative_binomial_distribution
Topics referred to by the same term
noncentral hypergeometric distribution Fisher's z-distribution Fisher's fiducial distribution Fisher–Bingham distribution F-distribution, also called
Fisher_distribution
Formula in probability theory
when s = 0 or s = n can be dealt with, we first go back to the hypergeometric distribution, denoted by H y p ( s | N , n , S ) {\displaystyle \mathrm {Hyp}
Rule_of_succession
the hypergeometric distribution, Bose–Einstein statistics and its limiting forms, the compound of the binomial distribution with the beta distribution, and
Divergence-from-randomness model
Divergence-from-randomness_model
Family of power series in mathematics
In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function
Generalized hypergeometric function
Generalized_hypergeometric_function
Type of probability distribution
distribution, but it is not called the Hypergeometric distribution, since that name is in use for an entirely different type of discrete distribution
Discrete phase-type distribution
Discrete_phase-type_distribution
beta distribution Noncentral chi distribution Noncentral chi-squared distribution Noncentral F-distribution Noncentral hypergeometric distributions Noncentral
List_of_statistics_articles
Type of data measuring one attribute
distribution Hypergeometric distribution Zeta distribution Uniform distribution (continuous) Normal distribution Gamma distribution Exponential distribution Weibull
Univariate_(statistics)
Sampling technique
replacement, the distribution is a binomial distribution. For a simple random sample without replacement, one obtains a hypergeometric distribution. Several efficient
Simple_random_sample
Family of continuous probability distributions
relation for values in the probability mass function of the hypergeometric distribution (which yields the linear-divided-by-quadratic structure). In
Pearson_distribution
Systematic classification of 12 related enumerative problems concerning two finite sets
multivariate hypergeometric distribution. Sampling without replacement where order does matter does not seem to correspond to a probability distribution. In all
Twelvefold_way
"noncentrality parameter": see noncentral hypergeometric distributions, for example. The noncentrality parameter of the t-distribution may be negative or positive while
Noncentral_distribution
Branch of discrete mathematics
distribution · Pascal's pyramid · Pascal's simplex Distributions Binomial distribution · Negative binomial distribution · Hypergeometric distribution
Combinatorics
Method for approximate evaluation of integrals
Fog, A. (2008), "Calculation Methods for Wallenius' Noncentral Hypergeometric Distribution", Communications in Statistics, Simulation and Computation, vol
Laplace's_method
Probability distribution
the confluent hypergeometric function with the Bessel functions. In free probability theory, the role of Wigner's semicircle distribution is analogous
Wigner semicircle distribution
Wigner_semicircle_distribution
Family of random graph models
independent edge generation, this model uses a multivariate hypergeometric distribution to represent the probability of an entire graph configuration
Configuration_model
Distributions in probability theory
without replacement, the distribution follows a multivariate hypergeometric distribution. Once again, let α 0 = ∑ α k {\displaystyle \alpha _{0}=\sum
Dirichlet-multinomial distribution
Dirichlet-multinomial_distribution
Compound probability distribution
Discrete Distributions, 2nd edition, Wiley ISBN 0-471-54897-9 (Section 6.2.3) Kemp, C.D.; Kemp, A.W. (1956) "Generalized hypergeometric distributions", Journal
Beta negative binomial distribution
Beta_negative_binomial_distribution
Probability distribution
characteristic function of the Dirichlet distribution is a confluent form of the Lauricella hypergeometric series. It is given by Phillips as C F ( s
Dirichlet_distribution
Branch of statistics
distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is
Mathematical_statistics
Probability distribution
of the hypergeometric function. For information on its inverse cumulative distribution function, see quantile function § Student's t-distribution. Certain
Student's_t-distribution
Function related to statistics and probability theory
totals leads to a conditional likelihood based on the non-central hypergeometric distribution. This form of conditioning is also the basis for Fisher's exact
Likelihood_function
Probability distribution
function. The characteristic function of the beta distribution is Kummer's confluent hypergeometric function (of the first kind): φ X ( α ; β ; t ) =
Beta_distribution
Family of probability distributions related to the normal distribution
Dirichlet-multinomial distributions. Other examples of distributions that are not exponential families are the F-distribution, Cauchy distribution, hypergeometric distribution
Exponential_family
Statistical test for analysis of contingency tables
milk first follows the hypergeometric distribution Hypergeometric ( 8 , 4 , 4 ) . {\displaystyle \ {\mbox{Hypergeometric}}(8,4,4)~.} Boschloo's test
Boschloo's_test
Software for statistical analysis of molecular evolution
algorithm is O(n!). The name for the distribution method is Hypergeometric Distribution (Hoffman). Tajima's Neutrality Test — The purpose of Tajima's
Molecular Evolutionary Genetics Analysis
Molecular_Evolutionary_Genetics_Analysis
number Gamma distribution Gamma function Gaussian binomial coefficient Gould's sequence Hyperfactorial Hypergeometric distribution Hypergeometric function
List of factorial and binomial topics
List_of_factorial_and_binomial_topics
Bioinformatics method
statistically overrepresented terms in the user's list of genes using hypergeometric distribution. MOET also displays the corresponding Bonferroni correction and
Gene_set_enrichment_analysis
multivariate integrals. Hypergeometric functions of a matrix argument have applications in random matrix theory. For example, the distributions of the extreme
Hypergeometric function of a matrix argument
Hypergeometric_function_of_a_matrix_argument
Animal population estimation method
ISBN 9780321021731. Chapman, D.G. (1951). Some properties of the hypergeometric distribution with applications to zoological sample censuses. UC Publications
Mark_and_recapture
Probability distribution
the Rice fading distribution", IEEE Communications Letters, March 2001, p. 92–94 Liu 2007 (in one of Horn's confluent hypergeometric functions with two
Rice_distribution
Probability distribution
noncentrality parameter μ can be expressed in several forms. The confluent hypergeometric function form of the density function is f ( x ) = Γ ( ν + 1 2 ) ν π
Noncentral_t-distribution
Concept in natural language processing
NASARI: Sparse vector representations constructed by applying the hypergeometric distribution over the Wikipedia corpus in combination with BabelNet taxonomy
Semantic_similarity
Probability distribution with more than one mode
a known density that can be expressed as a confluent hypergeometric function. The distribution of the reciprocal of a t distributed random variable is
Multimodal_distribution
Hypothesis test to compare the survival distributions of two samples
{\displaystyle i=1,2} , O i , j {\displaystyle O_{i,j}} follows a hypergeometric distribution with parameters N j {\displaystyle N_{j}} , N i , j {\displaystyle
Logrank_test
Detection of mRNA molecules
would see 40 instead of 1 due to pure chance. According to the hypergeometric distribution, one would expect to try about 10^57 times (10 followed by 56
Gene_expression_profiling
Surname list
Twilightning Wallenius' noncentral hypergeometric distribution, generalization of the hypergeometric distribution where items are sampled with bias Wallenius
Wallenius
Generalization of the one-dimensional normal distribution to higher dimensions
statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional
Multivariate normal distribution
Multivariate_normal_distribution
Generalization of Gaussian distribution
c ; z ) {\displaystyle {}_{2}F_{1}(a,b;c;z)} is the hypergeometric function. As the hypergeometric function is defined for |z| < 1 but x is unbounded,
Q-Gaussian_distribution
Quantitative analysis of law
consumption Risk compensation Challenging election results (Hypergeometric distribution) Condorcet's jury theorem Cost-benefit analysis of renewable
Jurimetrics
Probability distribution
where M ( a , b , z ) {\displaystyle M(a,b,z)} is Kummer's confluent hypergeometric function. The characteristic function is given by: φ ( t ; k ) = M (
Chi_distribution
Family of lifetime distributions with decreasing failure rate
1 {\displaystyle F_{2,1}} is a hypergeometric function. This function is also known as Barnes's extended hypergeometric function. The definition of F N
Exponential-logarithmic distribution
Exponential-logarithmic_distribution
Distribution of variables which satisfies a stability property under linear combinations
a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up
Stable_distribution
Probability distribution
1 {\displaystyle {}_{2}F_{1}} is the Gauss's hypergeometric function 2F1 . The beta prime distribution may also be reparameterized in terms of its mean
Beta_prime_distribution
Probability distribution
{1-\rho ^{2}}}.\end{aligned}}} The complex distribution has also been expressed with Kummer's confluent hypergeometric function or the Hermite function. This
Ratio_distribution
Concept in probability theory
posterior distribution p ( θ ∣ x ) {\displaystyle p(\theta \mid x)} is in the same probability distribution family as the prior probability distribution p (
Conjugate_prior
Topic in probability theory and statistics
the central limit theorem (CLT). Special case of distribution parametrization: X is a hypergeometric (m, N, n) random variable. If n and m are large compared
Relationships among probability distributions
Relationships_among_probability_distributions
Dutch psychometrician and statistician (1935–2018)
Molenaar, W. (1970). Approximations to the Poisson, Binomial and Hypergeometric Distribution Functions. Mathematisch Centrum. ISBN 978-90-6196-053-9. Fischer
Ivo_Molenaar
Grammatical analysis method family
statistics, namely the Fisher-Yates exact test based on the hypergeometric distribution; thus, unlike t-scores, z-scores, chi-square tests etc., the
Collostructional_analysis
Probability distribution
however, obtain the following formula in terms of the generalized hypergeometric function: F ( n ) = P ( X ≤ n ) = 1 − 1 F ν − 1 ( ; n + 2 , … , n +
Conway–Maxwell–Poisson distribution
Conway–Maxwell–Poisson_distribution
Statistics of spatial association
expectation of the local statistics are available based on the hypergeometric distribution but due to the multiple comparisons problem a permutation based
Join_count_statistic
Probability distribution in physics
{\tfrac {1}{2}}\chi ^{2})}}} where M(·,·,·) is the Kummer's confluent hypergeometric function.[circular reference] The variance is: σ 2 = c 2 ( χ 2 ) p +
ARGUS_distribution
Probability distribution
_{1}F_{2}} is a generalized hypergeometric function. Hann function Havercosine (hvc) Horst Rinne (2010). "Location-Scale Distributions – Linear Estimation and
Raised_cosine_distribution
Risk measure estimating the average loss in the worst tail of the distribution
{\displaystyle _{2}F_{1}} is the hypergeometric function. If the payoff of a portfolio X {\displaystyle X} follows lognormal distribution, i.e. the random variable
Expected_shortfall
Noncentral generalization of the chi-squared distribution
\Gamma (\nu +j+1)}}.} Using the relation between Bessel functions and hypergeometric functions, the pdf can also be written as: f X ( x ; k , λ ) = e − λ
Noncentral chi-squared distribution
Noncentral_chi-squared_distribution
Probability theory term
{10-x}{3-y}}}{\binom {10}{3}}}} for 0 ≤ y ≤ min ( 3, x ). It is the hypergeometric distribution H ( x; 3, 7 ), or equivalently, H ( 3; x, 10-x ). The corresponding
Conditioning_(probability)
Generating pseudo-random numbers that follow a probability distribution
generating pseudo-random numbers (PRN) that follow a given probability distribution. Methods are typically based on the availability of a uniformly distributed
Non-uniform random variate generation
Non-uniform_random_variate_generation
Kummer's function Riesz function Hypergeometric functions: Versatile family of power series. Confluent hypergeometric function Associated Legendre functions
List of mathematical functions
List_of_mathematical_functions
Probability distribution
}[(a)_{k}(b)_{k}/(c)_{k}]z^{k}/k!} is a Hypergeometric function. The Gamma/Gompertz distribution is a flexible distribution that can be skewed to the right or
Gamma/Gompertz_distribution
Probability distribution
product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given
Distribution of the product of two random variables
Distribution_of_the_product_of_two_random_variables
Family of probability distributions
1063/1.530917. hdl:2066/141604. S2CID 13934946. Exton, H. (1983), q-Hypergeometric Functions and Applications, New York: Halstead Press, Chichester: Ellis
Gaussian_q-distribution
Database of rat genomics
statistically overrepresented terms in the user's list of genes using hypergeometric distribution. MOET also displays the corresponding Bonferroni correction and
Rat_Genome_Database
Empirical law on the variance of species in a habitat
doi:10.1093/jee/84.1.140. Shiyomi M, Egawa T, Yamamoto Y (1998) Negative hypergeometric series and Taylor's power law in occurrence of plant populations in
Taylor's_law
Sequence of differential equation solutions
{1}{(1-t)^{\alpha +1}}}e^{-tx/(1-t)}.} Laguerre functions are defined by confluent hypergeometric functions and Kummer's transformation as L n ( α ) ( x ) := ( n + α
Laguerre_polynomials
polynomials Gaussian q-distribution q-exponential distribution q-Weibull distribution Tsallis q-Gaussian Tsallis entropy Basic hypergeometric series Elliptic
List_of_q-analogs
Biology database
predefined set (pathway / NEST), a P-value is computed based on the hypergeometric distribution. It reflects the significance of the observed overlap between
ConsensusPathDB
Probability distribution
including the half-normal distribution, truncated normal distribution, gamma distribution, and square root of the gamma distribution, all of which are special
Modified half-normal distribution
Modified_half-normal_distribution
Type of analysis in molecular biology
test producing p-values (Fisher's exact test or the test using hypergeometric distribution). This method identifies FGS by considering their relative positions
Pathway_analysis
terms of hypergeometric functions). The entire class of discrete-stable distributions can be formed as Poisson compound probability distribution where the
Discrete-stable_distribution
Probability distribution
noncentral beta distribution is a continuous probability distribution that is a noncentral generalization of the (central) beta distribution. The noncentral
Noncentral_beta_distribution
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