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MULTIVARIATE GAMMA-FUNCTION

  • Multivariate gamma function
  • Multivariate generalization of the gamma function

    In mathematics, the multivariate gamma function Γp is a generalization of the gamma function. It is useful in multivariate statistics, appearing in the

    Multivariate gamma function

    Multivariate_gamma_function

  • Gamma function
  • Extension of the factorial function

    approximation Multiple gamma function Multivariate gamma function p-adic gamma function Pochhammer k-symbol Polygamma function q-gamma function Ramanujan's master

    Gamma function

    Gamma function

    Gamma_function

  • List of mathematical functions
  • function, Polygamma function Incomplete beta function Incomplete gamma function K-function Multivariate gamma function: A generalization of the Gamma

    List of mathematical functions

    List_of_mathematical_functions

  • Wishart distribution
  • Generalization of gamma distribution to multiple dimensions

    and Γp is the multivariate gamma function defined as Γ p ( n 2 ) = π p ( p − 1 ) / 4 ∏ j = 1 p Γ ( n 2 − j − 1 2 ) . {\displaystyle \Gamma _{p}\left({\frac

    Wishart distribution

    Wishart_distribution

  • Beta function
  • Mathematical function

    the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial

    Beta function

    Beta function

    Beta_function

  • Inverse-Wishart distribution
  • Probability distribution

    the determinant, and Γ p ( ⋅ ) {\displaystyle \Gamma _{p}(\cdot )} is the multivariate gamma function. If X ∼ W ( Σ , ν ) {\displaystyle {\mathbf {X}

    Inverse-Wishart distribution

    Inverse-Wishart_distribution

  • Normal-inverse-gamma distribution
  • Family of multivariate continuous probability distributions

    statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions

    Normal-inverse-gamma distribution

    Normal-inverse-gamma distribution

    Normal-inverse-gamma_distribution

  • Inverse-gamma distribution
  • Two-parameter family of continuous probability distributions

    scaled inverse chi-squared distribution. The inverse gamma distribution's probability density function is defined over the support x > 0 {\displaystyle x>0}

    Inverse-gamma distribution

    Inverse-gamma distribution

    Inverse-gamma_distribution

  • Characteristic function (probability theory)
  • Fourier transform of the probability density function

    characteristic functions generalizes to multivariate random variables and more complicated random elements. The argument of the characteristic function will always

    Characteristic function (probability theory)

    Characteristic function (probability theory)

    Characteristic_function_(probability_theory)

  • Multivariate stable distribution
  • Concept in probability theory

    terms of its characteristic function. The multivariate stable distribution can also be thought as an extension of the multivariate normal distribution. It

    Multivariate stable distribution

    Multivariate stable distribution

    Multivariate_stable_distribution

  • Special functions
  • Mathematical functions having established names and notations

    to Atle Selberg, the multivariate gamma function, and types of Bessel functions. The NIST Digital Library of Mathematical Functions has a section covering

    Special functions

    Special_functions

  • Gamma distribution
  • Probability distribution

    {\gamma (\alpha ,\beta x)}{\Gamma (\alpha )}},} where γ ( α , β x ) {\displaystyle \gamma (\alpha ,\beta x)} is the lower incomplete gamma function. If

    Gamma distribution

    Gamma distribution

    Gamma_distribution

  • Generating function
  • Formal power series

    generating function in several variables can be generalized to arrays with multiple indices. These non-polynomial double sum examples are called multivariate generating

    Generating function

    Generating_function

  • Complex inverse Wishart distribution
  • where C Γ p ( ν ) {\displaystyle {\mathcal {C}}\Gamma _{p}(\nu )} is the complex multivariate Gamma function C Γ p ( ν ) = π 1 2 p ( p − 1 ) ∏ j = 1 p Γ (

    Complex inverse Wishart distribution

    Complex_inverse_Wishart_distribution

  • Cauchy distribution
  • Probability distribution

    function of a multivariate Cauchy distribution is given by: φ X ( t ) = e i x 0 ( t ) − γ ( t ) , {\displaystyle \varphi _{X}(t)=e^{ix_{0}(t)-\gamma (t)}

    Cauchy distribution

    Cauchy distribution

    Cauchy_distribution

  • Binomial coefficient
  • Number of subsets of a given size

    generalized to two real or complex valued arguments using the gamma function or beta function via ( x y ) = Γ ( x + 1 ) Γ ( y + 1 ) Γ ( x − y + 1 ) = 1 (

    Binomial coefficient

    Binomial coefficient

    Binomial_coefficient

  • Multivariate t-distribution
  • Multivariable generalization of the Student's t-distribution

    In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization

    Multivariate t-distribution

    Multivariate_t-distribution

  • Complex Wishart distribution
  • Probability distribution on complex matrices

    {\mathcal {C}}{\widetilde {\Gamma }}_{p}^{}(n)=\pi ^{p(p-1)/2}\prod _{j=1}^{p}\Gamma (n-j+1)} is the complex multivariate Gamma function. Using the trace rotation

    Complex Wishart distribution

    Complex_Wishart_distribution

  • Matrix variate beta distribution
  • Generalization of beta distribution

    is the multivariate beta function: β p ( a , b ) = Γ p ( a ) Γ p ( b ) Γ p ( a + b ) {\displaystyle \beta _{p}\left(a,b\right)={\frac {\Gamma _{p}\left(a\right)\Gamma

    Matrix variate beta distribution

    Matrix_variate_beta_distribution

  • Generalized multivariate log-gamma distribution
  • probability theory and statistics, the generalized multivariate log-gamma (G-MVLG) distribution is a multivariate distribution introduced by Demirhan and Hamurkaroglu

    Generalized multivariate log-gamma distribution

    Generalized_multivariate_log-gamma_distribution

  • Holomorphic function
  • Complex-differentiable (mathematical) function

    {\displaystyle U} ⁠. Osgood's lemma shows (using the multivariate Cauchy integral formula) that, for a continuous function ⁠ f {\displaystyle f} ⁠, this is equivalent

    Holomorphic function

    Holomorphic function

    Holomorphic_function

  • Matrix F-distribution
  • Multivariate continuous probability distribution

    | {\displaystyle |\cdot |} is the determinant, Γp(⋅) is the multivariate gamma function, and I p {\displaystyle {\textbf {I}}_{p}} is the p × p identity

    Matrix F-distribution

    Matrix_F-distribution

  • Sinc function
  • Special mathematical function defined as sin(x)/x

    }\left(1-{\frac {x^{2}}{n^{2}}}\right)} and is related to the gamma function Γ(x), as well as to Gauss' Pi function, through Euler's reflection formula: sin ⁡ ( π x

    Sinc function

    Sinc function

    Sinc_function

  • Student's t-distribution
  • Probability distribution

    is the number of degrees of freedom, and Γ {\displaystyle \Gamma } is the gamma function. This may also be written as f ( t ) = 1 ν B ( 1 2 , ν 2 ) (

    Student's t-distribution

    Student's t-distribution

    Student's_t-distribution

  • Multivariate normal distribution
  • Generalization of the one-dimensional normal distribution to higher dimensions

    In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization

    Multivariate normal distribution

    Multivariate normal distribution

    Multivariate_normal_distribution

  • Q-function
  • Statistics function

    {\displaystyle \gamma >0} . As in the one dimensional case, there is no simple analytical formula for the Q-function. Nevertheless, the Q-function can be approximated

    Q-function

    Q-function

    Q-function

  • Generalized beta distribution
  • Probability distribution

    {\displaystyle y_{i}} for all y i {\displaystyle y_{i}} . The multivariate generalized gamma (MGG) pdf can be derived from the MGB pdf by substituting b

    Generalized beta distribution

    Generalized_beta_distribution

  • Weibull distribution
  • Continuous probability distribution

    {\displaystyle \gamma _{2}={\frac {-6\Gamma _{1}^{4}+12\Gamma _{1}^{2}\Gamma _{2}-3\Gamma _{2}^{2}-4\Gamma _{1}\Gamma _{3}+\Gamma _{4}}{[\Gamma _{2}-\Gamma _{1}^{2}]^{2}}}}

    Weibull distribution

    Weibull distribution

    Weibull_distribution

  • Dirichlet distribution
  • Probability distribution

    The normalizing constant is the multivariate beta function, which can be expressed in terms of the gamma function: B ( α ) = ∏ i = 1 K Γ ( α i ) Γ (

    Dirichlet distribution

    Dirichlet distribution

    Dirichlet_distribution

  • List of factorial and binomial topics
  • theorem Multiplicities of entries in Pascal's triangle Multiset Multivariate gamma function Narayana numbers Negative binomial distribution Nörlund–Rice

    List of factorial and binomial topics

    List_of_factorial_and_binomial_topics

  • Standard score
  • How many standard deviations apart from the mean an observed datum is

    test-takers who received lower scores than students A and B. "For some multivariate techniques such as multidimensional scaling and cluster analysis, the

    Standard score

    Standard score

    Standard_score

  • Function of several real variables
  • Mathematical function with multiple real-number arguments

    In mathematics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being

    Function of several real variables

    Function_of_several_real_variables

  • Chi-squared distribution
  • Probability distribution and special case of gamma distribution

    incomplete gamma function and P ( s , t ) {\textstyle P(s,t)} is the regularized gamma function. In a special case of k = 2 {\displaystyle k=2} this function has

    Chi-squared distribution

    Chi-squared distribution

    Chi-squared_distribution

  • Weierstrass–Mandelbrot function
  • Multifractal function used in terrain modeling and simulation

    "Weierstrass Function". MathWorld. Multifractal terrain generation paper on arXiv Fractal terrain for vehicle simulation Multivariate W-M function on ResearchGate

    Weierstrass–Mandelbrot function

    Weierstrass–Mandelbrot function

    Weierstrass–Mandelbrot_function

  • Normal distribution
  • Probability distribution

    variance σ2, a combined (multivariate) conjugate prior is placed over the mean and variance, consisting of a normal-inverse-gamma distribution. Logically

    Normal distribution

    Normal distribution

    Normal_distribution

  • Matrix gamma distribution
  • Generalization of gamma distribution

    similarly, e.g. as the conjugate prior of the precision matrix of a multivariate normal distribution and matrix normal distribution. The compound distribution

    Matrix gamma distribution

    Matrix_gamma_distribution

  • Matrix t-distribution
  • Concept in statistics

    {\Sigma }}|^{-{\frac {p}{2}}}.} Here Γ p {\displaystyle \Gamma _{p}} is the multivariate gamma function. If X ∼ T n × p ( ν , M , Σ , Ω ) {\displaystyle \mathbf

    Matrix t-distribution

    Matrix_t-distribution

  • Conjugate prior
  • Concept in probability theory

    respectively, or to the multivariate normal distribution and multivariate t-distribution in the multivariate cases. In terms of the inverse gamma, β {\displaystyle

    Conjugate prior

    Conjugate_prior

  • Probability distribution
  • Mathematical function for the probability a given outcome occurs in an experiment

    to the inverse of the covariance matrix of a multivariate normal distribution; generalization of the gamma distribution The cache language models and other

    Probability distribution

    Probability distribution

    Probability_distribution

  • Matérn covariance function
  • Tool in multivariate statistical analysis

    a covariance function used in spatial statistics, geostatistics, machine learning, image analysis, and other applications of multivariate statistical analysis

    Matérn covariance function

    Matérn_covariance_function

  • Quantile function
  • Statistical function that defines the quantiles of a probability distribution

    focusing increasing attention on methods based on quantile functions, as they work well with multivariate techniques based on either copula or quasi-Monte-Carlo

    Quantile function

    Quantile function

    Quantile_function

  • Confluent hypergeometric function
  • Solution of a confluent hypergeometric equation

    gamma function Laguerre polynomials Parabolic cylinder function (or Weber function) Poisson–Charlier function Toronto functions Whittaker functions

    Confluent hypergeometric function

    Confluent hypergeometric function

    Confluent_hypergeometric_function

  • Inverse matrix gamma distribution
  • Probability distribution

    similarly, e.g. as the conjugate prior of the covariance matrix of a multivariate normal distribution or matrix normal distribution. The compound distribution

    Inverse matrix gamma distribution

    Inverse_matrix_gamma_distribution

  • Pareto distribution
  • Probability distribution

    {y^{\gamma _{1}-1}(1-y)^{\gamma _{2}-1}}{B(\gamma _{1},\gamma _{2})}},\qquad 0<y<1;\gamma _{1},\gamma _{2}>0,} where B( ) is the beta function. If W = μ + σ ( Y

    Pareto distribution

    Pareto distribution

    Pareto_distribution

  • Combinatorics
  • Branch of discrete mathematics

    combinatorics, which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic

    Combinatorics

    Combinatorics

  • Copula (statistics)
  • Statistical distribution for dependence between random variables

    In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each

    Copula (statistics)

    Copula_(statistics)

  • Autoregressive model
  • Representation of a type of random process

    {\begin{bmatrix}\gamma _{1}\\\gamma _{2}\\\gamma _{3}\\\vdots \\\gamma _{p}\\\end{bmatrix}}={\begin{bmatrix}\gamma _{0}&\gamma _{-1}&\gamma _{-2}&\cdots \\\gamma _{1}&\gamma

    Autoregressive model

    Autoregressive_model

  • Generalized integer gamma distribution
  • density function is f X ( x ) = λ r Γ ( r ) e − λ x x r − 1             ( x > 0 ; λ , r > 0 ) {\displaystyle f_{X}^{}(x)={\frac {\lambda ^{r}}{\Gamma (r)}}\

    Generalized integer gamma distribution

    Generalized_integer_gamma_distribution

  • List of probability distributions
  • generalization of the beta negative binomial distribution. The generalized multivariate log-gamma distribution The Marshall–Olkin exponential distribution The

    List of probability distributions

    List_of_probability_distributions

  • Beta distribution
  • Probability distribution

    -1}\end{aligned}}} where Γ ( z ) {\displaystyle \Gamma (z)} is the gamma function. The beta function, B {\displaystyle \mathrm {B} } , is a normalization

    Beta distribution

    Beta distribution

    Beta_distribution

  • Exponential family
  • Family of probability distributions related to the normal distribution

    first need to expand the part of the log-partition function that involves the multivariate gamma function: log ⁡ Γ p ( a ) = log ⁡ ( π p ( p − 1 ) 4 ∏ j =

    Exponential family

    Exponential_family

  • Generalized normal distribution
  • Probability distribution

    ∈ ( 0 , 1 ] ∪ { 2 } {\displaystyle \beta \in (0,1]\cup \{2\}} ⁠. The multivariate generalized normal distribution, i.e. the product of n {\displaystyle

    Generalized normal distribution

    Generalized_normal_distribution

  • Credible interval
  • Concept in Bayesian statistics

    γ {\displaystyle \gamma } -Smallest Credible Sets ( γ {\displaystyle \gamma } -SCS) can easily be generalized to the multivariate case, and are bounded

    Credible interval

    Credible interval

    Credible_interval

  • Chi distribution
  • Probability distribution

    Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable and the origin. The chi distribution describes

    Chi distribution

    Chi distribution

    Chi_distribution

  • Analytic combinatorics
  • Field of combinatorics using complex analysis

    earliest work on multivariate generating functions started in the 1970s using probabilistic methods. Development of further multivariate techniques started

    Analytic combinatorics

    Analytic_combinatorics

  • Dirichlet-multinomial distribution
  • Distributions in probability theory

    statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers

    Dirichlet-multinomial distribution

    Dirichlet-multinomial_distribution

  • Logarithmically concave function
  • Type of mathematical function

    density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any

    Logarithmically concave function

    Logarithmically_concave_function

  • Uniform distribution on a Stiefel manifold
  • Matrix-variate probability distribution

    n}}(X'dX)={\frac {2^{n}\pi ^{pn/2}}{\Gamma _{n}({\tfrac {1}{2}}p)}},} where Γ n {\displaystyle \Gamma _{n}} is the multivariate gamma function. The uniform distribution

    Uniform distribution on a Stiefel manifold

    Uniform_distribution_on_a_Stiefel_manifold

  • Likelihood function
  • Function related to statistics and probability theory

    which is calculated via Bayes' rule. The likelihood function, parameterized by a (possibly multivariate) parameter θ {\textstyle \theta } , is usually defined

    Likelihood function

    Likelihood_function

  • Multivariate Laplace distribution
  • Probability distribution

    typical characterization of the symmetric multivariate Laplace distribution has the characteristic function: φ ( t ; μ , Σ ) = exp ⁡ ( i μ ′ t ) 1 + 1

    Multivariate Laplace distribution

    Multivariate_Laplace_distribution

  • Skew normal distribution
  • Probability distribution

    developed in Chan and Tong (1986), which applies to multivariate cases beyond normality, e.g. skew multivariate t distribution and others. The distribution is

    Skew normal distribution

    Skew normal distribution

    Skew_normal_distribution

  • Normal-inverse-Wishart distribution
  • Multivariate parameter family of continuous probability distributions

    }}_{0})\right\}} Here Γ D [ ⋅ ] {\displaystyle \Gamma _{D}[\cdot ]} is the multivariate gamma function and T r ( Ψ ) {\displaystyle Tr({\boldsymbol {\Psi

    Normal-inverse-Wishart distribution

    Normal-inverse-Wishart_distribution

  • Hessian matrix
  • Matrix of second derivatives

    differential calculus with applications in the multivariate linear model and its diagnostics". Journal of Multivariate Analysis. 188 104849. doi:10.1016/j.jmva

    Hessian matrix

    Hessian_matrix

  • Hinge loss
  • Loss function in machine learning

    loss function with γ = 2 {\displaystyle \gamma =2} , specifically L ( t , y ) = 4 ℓ 2 ( y ) {\displaystyle L(t,y)=4\ell _{2}(y)} . Multivariate adaptive

    Hinge loss

    Hinge loss

    Hinge_loss

  • Gaussian process
  • Statistical model

    space), such that every finite collection of those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint

    Gaussian process

    Gaussian_process

  • Gaussian function
  • Mathematical function

    affine shape adaptation. Also see multivariate normal distribution. A more general formulation of a Gaussian function with a flat-top and Gaussian fall-off

    Gaussian function

    Gaussian_function

  • Gaussian integral
  • Integral of the Gaussian function, equal to sqrt(π)

    t {\textstyle \Gamma (z)=\int _{0}^{\infty }t^{z-1}e^{-t}dt} is the gamma function. More generally, ∫ 0 ∞ x n e − a x b d x = Γ ( ( n + 1 ) / b ) b a (

    Gaussian integral

    Gaussian integral

    Gaussian_integral

  • List of statistics articles
  • method of moments Generalized multidimensional scaling Generalized multivariate log-gamma distribution Generalized normal distribution Generalized p-value

    List of statistics articles

    List_of_statistics_articles

  • Taylor's theorem
  • Approximation of a function by a polynomial

    mathematical physics. Taylor's theorem also generalizes to multivariate and vector valued functions. It provided the mathematical basis for some landmark early

    Taylor's theorem

    Taylor's theorem

    Taylor's_theorem

  • Exponential distribution
  • Probability distribution

    distributions, such as the normal, binomial, gamma, and Poisson distributions. The probability density function (pdf) of an exponential distribution is f

    Exponential distribution

    Exponential distribution

    Exponential_distribution

  • Integration by parts
  • Mathematical method in calculus

    several such pairings possible in multivariate calculus, involving a scalar-valued function u and vector-valued function (vector field) V. The product rule

    Integration by parts

    Integration_by_parts

  • Multivariate Pareto distribution
  • In statistics, a multivariate Pareto distribution is a multivariate extension of a univariate Pareto distribution. There are several different types of

    Multivariate Pareto distribution

    Multivariate_Pareto_distribution

  • Poisson distribution
  • Discrete probability distribution

    using the lgamma function in the C standard library (C99 version) or R, the gammaln function in MATLAB or SciPy, or the log_gamma function in Fortran 2008

    Poisson distribution

    Poisson distribution

    Poisson_distribution

  • Chebyshev's inequality
  • Bound on probability of a random variable being far from its mean

    {\kappa -\gamma ^{2}-1}{(\kappa -\gamma ^{2}-1)(1+k^{2})+(k^{2}-k\gamma -1)}}.} The necessity of k 2 − k γ − 1 > 0 {\displaystyle k^{2}-k\gamma -1>0} may

    Chebyshev's inequality

    Chebyshev's_inequality

  • Correlation
  • Statistical relationship

    variance) is only a sufficient statistic if the data is drawn from a multivariate normal distribution. As a result, the Pearson correlation coefficient

    Correlation

    Correlation

    Correlation

  • M-estimator
  • Class of statistical estimators

    }}_{n},{\hat {\gamma }}_{n}):=\mathop {\arg \max } _{\beta ,\gamma }\sum _{i=1}^{N}\displaystyle q(w_{i},\beta ,\gamma )} Assuming the function q is differentiable

    M-estimator

    M-estimator

  • Correlation coefficient
  • Numerical measure of a statistical relationship between variables

    data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.[citation needed] Several types

    Correlation coefficient

    Correlation_coefficient

  • Generalized linear model
  • Class of statistical models

    canonical link functions and their inverses (sometimes referred to as the mean function, as done here). In the cases of the exponential and gamma distributions

    Generalized linear model

    Generalized_linear_model

  • General linear model
  • Statistical linear model

    The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models

    General linear model

    General_linear_model

  • Moment generating function
  • Concept in probability theory and statistics

    theory and statistics, the moment generating function of a real-valued random variable is a generating function that provides an alternative specification

    Moment generating function

    Moment_generating_function

  • Mathematical statistics
  • Branch of statistics

    or multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution

    Mathematical statistics

    Mathematical statistics

    Mathematical_statistics

  • Standard deviation
  • Measure of variation in statistics

    the gamma function, and equals: c 4 ( N ) = 2 N − 1 Γ ( N 2 ) Γ ( N − 1 2 ) . {\displaystyle c_{4}(N)\,=\,{\sqrt {\frac {2}{N-1}}}\,\,\,{\frac {\Gamma {\left({\frac

    Standard deviation

    Standard deviation

    Standard_deviation

  • Gumbel distribution
  • Particular case of the generalized extreme value distribution

    distributions. Theory related to the generalized multivariate log-gamma distribution provides a multivariate version of the Gumbel distribution. Gumbel has

    Gumbel distribution

    Gumbel distribution

    Gumbel_distribution

  • Robust statistics
  • Type of statistics

    Γ , S ) = ( R , B ) {\displaystyle (\Gamma ,S)=(\mathbb {R} ,{\mathcal {B}})} , The empirical influence function is defined as follows. Let n ∈ N ∗ {\displaystyle

    Robust statistics

    Robust_statistics

  • Distribution of the product of two random variables
  • Probability distribution

    function route is favorable. If we define y ~ = − y {\displaystyle {\tilde {y}}=-y} then c ( y ~ ) {\displaystyle c({\tilde {y}})} above is a Gamma distribution

    Distribution of the product of two random variables

    Distribution_of_the_product_of_two_random_variables

  • Nelder–Mead method
  • Numerical optimization algorithm

    Murray, Walter; Wright, Margaret H. (1981). "Methods for Multivariate Non-Smooth Functions". Practical Optimization. New York: Academic Press. pp. 93–96

    Nelder–Mead method

    Nelder–Mead method

    Nelder–Mead_method

  • Pearson correlation coefficient
  • Measure of linear correlation

    \Gamma } is the gamma function and 2 F 1 ( a , b ; c ; z ) {\displaystyle {}_{2}\mathrm {F} _{1}(a,b;c;z)} is the Gaussian hypergeometric function. In

    Pearson correlation coefficient

    Pearson correlation coefficient

    Pearson_correlation_coefficient

  • Complex normal distribution
  • Statistical distribution of complex random variables

    {\begin{aligned}&\Gamma =V_{XX}+V_{YY}+i(V_{YX}-V_{XY}),\\&C=V_{XX}-V_{YY}+i(V_{YX}+V_{XY}).\end{aligned}}} The probability density function for complex normal

    Complex normal distribution

    Complex_normal_distribution

  • FKG inequality
  • Correlation inequality

    chain coupling argument. The lattice condition for μ is also called multivariate total positivity, and sometimes the strong FKG condition; the term (multiplicative)

    FKG inequality

    FKG_inequality

  • Maxwell–Boltzmann distribution
  • Specific probability distribution function, important in physics

    {a+1}{2}}{\frac {\Gamma {\left({\frac {a+1}{2}}\right)}}{2}}\end{aligned}}} where Γ ( z ) {\displaystyle \Gamma (z)} is the Gamma function. This result can

    Maxwell–Boltzmann distribution

    Maxwell–Boltzmann distribution

    Maxwell–Boltzmann_distribution

  • Poisson regression
  • Statistical model for count data

    2021). "Is eliciting dependency worth the effort? A study for the multivariate Poisson-Gamma probability model". Proceedings of the Institution of Mechanical

    Poisson regression

    Poisson_regression

  • Empirical Bayes method
  • Bayesian statistical inference method

    (y|x)(x-y)} by direct calculation with the probability density function of multivariate gaussians. Integrating over ρ ( x ) d x {\displaystyle \rho (x)dx}

    Empirical Bayes method

    Empirical_Bayes_method

  • Split normal distribution
  • {\text{where}}\quad \beta ={\frac {\pi \xi ^{2}}{2\sigma ^{2}}}.\end{aligned}}} The multivariate generalization of the split normal distribution was proposed by Villani

    Split normal distribution

    Split_normal_distribution

  • Elliptical distribution
  • Family of distributions that generalize the multivariate normal distribution

    evaluate proposed multivariate-statistical procedures. Elliptical distributions are defined in terms of the characteristic function of probability theory

    Elliptical distribution

    Elliptical_distribution

  • Univariate (statistics)
  • Type of data measuring one attribute

    Univariate analysis can yield misleading results in cases in which multivariate analysis is more appropriate. Central tendency is one of the most common

    Univariate (statistics)

    Univariate_(statistics)

  • Contingency table
  • Table that displays the frequency of variables

    or crosstab) is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. They are heavily used in survey

    Contingency table

    Contingency_table

  • Central limit theorem
  • Fundamental theorem in probability theory and statistics

    multidimensional central limit theorem states that when scaled, sums converge to a multivariate normal distribution. Summation of these vectors is done component-wise

    Central limit theorem

    Central limit theorem

    Central_limit_theorem

  • Maximum likelihood estimation
  • Method of estimating the parameters of a statistical model, given observations

    {\Sigma }}} . The joint probability density function of these n random variables then follows a multivariate normal distribution given by: f ( y 1 , …

    Maximum likelihood estimation

    Maximum_likelihood_estimation

  • Kriging
  • Method of interpolation

    Bayes linear statistics Gaussian process Multivariate interpolation Nonparametric regression Radial basis function interpolation Space mapping Spatial dependence

    Kriging

    Kriging

    Kriging

  • Exponential dispersion model
  • Set of probability distributions

    family. In the multivariate case, the n-dimensional random variable X {\displaystyle \mathbf {X} } has a probability density function of the following

    Exponential dispersion model

    Exponential_dispersion_model

AI & ChatGPT searchs for online references containing MULTIVARIATE GAMMA-FUNCTION

MULTIVARIATE GAMMA-FUNCTION

AI search references containing MULTIVARIATE GAMMA-FUNCTION

MULTIVARIATE GAMMA-FUNCTION

  • Gamya | கம்யா
  • Girl/Female

    Tamil

    Gamya | கம்யா

    Beautiful, A destiny

    Gamya | கம்யா

  • GEMMA
  • Female

    English

    GEMMA

    Italian name GEMMA means "precious stone."

    GEMMA

  • Amma
  • Boy/Male

    Indian

    Amma

    Supreme god.

    Amma

  • Jenner
  • Surname or Lastname

    English (chiefly Kent and Sussex)

    Jenner

    English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.

    Jenner

  • Kamma
  • Girl/Female

    Danish, Indian, Latin, Sanskrit, Swedish

    Kamma

    Loveable; Desire

    Kamma

  • Gemma
  • Girl/Female

    French Latin Italian

    Gemma

    Jewel.

    Gemma

  • Farqadin
  • Boy/Male

    Arabic

    Farqadin

    Two Bright Stars Near the Pole; Beta and Gama in Ursa Minor

    Farqadin

  • Gates
  • Surname or Lastname

    English

    Gates

    English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.

    Gates

  • Mammen
  • Surname or Lastname

    German

    Mammen

    German : East Frisian patronymic from the nursery name Mamme, linked to Middle High German mamme, memme ‘mother’s breast’ (Latin mamma).English (of Norman origin) : from the Old French personal name Maismon, Maimon, of unknown etymology.Indian (Kerala) : variant of Thomas among Kerala Christians, with the Tamil-Malayalam third person masculine singular suffix -n. It is only found as a personal name in Kerala, but in the U.S. has come to be used as a family name among Kerala Christians.

    Mammen

  • Fuller
  • Surname or Lastname

    English

    Fuller

    English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.

    Fuller

  • Damma
  • Girl/Female

    Gujarati, Hindu, Indian

    Damma

    The Soothing Voice

    Damma

  • JEMMA
  • Female

    English

    JEMMA

    Variant spelling of Italian Gemma, JEMMA means "precious stone."

    JEMMA

  • Samma
  • Girl/Female

    Arabic, Indian, Kashmiri

    Samma

    Beautiful Sky

    Samma

  • Tamma
  • Girl/Female

    Hebrew

    Tamma

    Without flaw.

    Tamma

  • Gemma
  • Girl/Female

    African, American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Irish, Italian, Jamaican, Latin

    Gemma

    Jewel; Precious Stone; Gem

    Gemma

  • Tamma
  • Girl/Female

    Australian, French, Hebrew

    Tamma

    Without Flaw; Palm Tree; Perfect

    Tamma

  • Gamya
  • Girl/Female

    Hindu, Indian, Kannada, Telugu

    Gamya

    Beautiful; A Destiny

    Gamya

  • Amma
  • Boy/Male

    African, British, English, Indian

    Amma

    Mother; God-like

    Amma

  • Gammon
  • Surname or Lastname

    English

    Gammon

    English : variant of Game.English : from Anglo-Norman French gambon ‘ham’, a diminutive of gambe, Norman-Picard form of Old French jambe ‘leg’ (Late Latin gamba), hence probably a nickname for someone with some peculiarity of the legs or gait.

    Gammon

  • Amma
  • Girl/Female

    Norse

    Amma

    Grandmother.

    Amma

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Online names & meanings

  • Mahin
  • Girl/Female

    Arabic, Farsi, Gujarati, Indian, Iranian, Kannada, Muslim, Parsi, Zoroastrian

    Mahin

    Greatest; Related to the Moon

  • Cong
  • Surname or Lastname

    English

    Cong

    English : unexplained.Chinese : from an ancient area named Cong Yang, whose residents adopted the surname.Vietnamese : unexplained.

  • Jastaran
  • Boy/Male

    Indian, Punjabi, Sikh

    Jastaran

    Floating in Glory

  • AbulHaisam
  • Boy/Male

    Arabic, Muslim

    AbulHaisam

    A Sahabi; Also a Great Scholar of History

  • Lowrance
  • Surname or Lastname

    English

    Lowrance

    English : variant spelling of Lawrence.

  • Sanjay
  • Boy/Male

    Bengali, British, Celebrity, English, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu, Traditional

    Sanjay

    Victory; Lord Shiva; Dhritarashtra's Charioteer; Triumphant; Caring; Victorious

  • Machi
  • Biblical

    Machi

    poor; a smiter,decrease

  • Hozaifah |
  • Boy/Male

    Muslim

    Hozaifah |

    A companion of the prophet

  • Satwant
  • Boy/Male

    Sikh

    Satwant

    Truthfulness

  • Brasil
  • Boy/Male

    Irish Celtic

    Brasil

    War.

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Other words and meanings similar to

MULTIVARIATE GAMMA-FUNCTION

AI search in online dictionary sources & meanings containing MULTIVARIATE GAMMA-FUNCTION

MULTIVARIATE GAMMA-FUNCTION

  • Gumma
  • n.

    A kind of soft tumor, usually of syphilitic origin.

  • Yamma
  • n.

    The llama.

  • Mammae
  • pl.

    of Mamma

  • Mamma
  • n.

    Mother; -- word of tenderness and familiarity.

  • Gummous
  • a.

    Of or pertaining to a gumma.

  • Mam
  • n.

    Mamma.

  • Multistriate
  • a.

    Having many streaks.

  • Gemma
  • n.

    A bud spore; one of the small spores or buds in the reproduction of certain Protozoa, which separate one at a time from the parent cell.

  • Gamma
  • n.

    The third letter (/, / = Eng. G) of the Greek alphabet.

  • Gemma
  • n.

    A leaf bud, as distinguished from a flower bud.

  • Multiradiate
  • a.

    Having many rays.

  • Multicarinate
  • a.

    Many-keeled.

  • Baritone
  • n.

    The viola di gamba, now entirely disused.

  • Mama
  • n.

    See Mamma.

  • Gamba
  • n.

    A viola da gamba.

  • Mammy
  • n.

    A child's name for mamma, mother.

  • Gummatous
  • a.

    Belonging to, or resembling, gumma.

  • Gemmae
  • pl.

    of Gemma

  • Mamma
  • n.

    A glandular organ for secreting milk, characteristic of all mammals, but usually rudimentary in the male; a mammary gland; a breast; under; bag.

  • Gummata
  • pl.

    of Gumma