In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization...

Multinomial may refer to: Multinomial theorem, and the multinomial coefficient Multinomial distribution Multinomial logistic regression Multinomial test...

algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ⁠ ( x...

In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts...

later rediscovered by Euler, is a very simple application of the multinomial theorem, which states ( x 1 + x 2 + ⋯ + x m ) n = ∑ k 1 , k 2 , … , k m k...

representation of an integer Mahler's theorem Multinomial distribution Multinomial coefficient, Multinomial formula, Multinomial theorem Multiplicities of entries...

(Ramsey theory) Multinomial theorem (algebra, combinatorics) Mycielski's theorem (graph theory) Nicomachus's theorem (number theory) Ore's theorem (graph theory)...

dimensions; for σ = 1 {\displaystyle \sigma =1} , its expansion using the multinomial theorem is: exp ⁡ ( − 1 2 ‖ x − x ′ ‖ 2 ) = exp ⁡ ( 2 2 x ⊤ x ′ − 1 2 ‖ x...

In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest...

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more...

(or R n → R {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} } ). Multinomial theorem ( ∑ i = 1 n x i ) k = ∑ | α | = k ( k α ) x α {\displaystyle \left(\sum...

In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree...

the quadratic kernel. After using the multinomial theorem (twice—the outermost application is the binomial theorem) and regrouping, K ( x , y ) = ( ∑ i...

probability theory, Donsker's theorem (also known as Donsker's invariance principle, or the functional central limit theorem), named after Monroe D. Donsker...

combinatorisch-analytischer Abhandlungen, which contained a claim that de Moivre's multinomial theorem was “the most important proposition in all of mathematical analysis”...

In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite...

de Moivre also generalised Newton's noteworthy binomial theorem into the multinomial theorem. The Royal Society became apprised of this method in 1697...

{S_{2}(3)+S_{2}(7)-S_{2}(10)}{2-1}}={\dfrac {2+3-2}{2-1}}=3.} Kummer's theorem can be generalized to multinomial coefficients ( n m 1 , … , m k ) = n ! m 1 ! ⋯ m k ! {\displaystyle...

approximation theorem Hilbert's paradox of the Grand Hotel Multinomial theorem Pochhammer symbol Ramsey's theorem Herstein 1964, p. 90 Rittaud, Benoît; Heeffer, Albrecht...

With a multinomial event model, samples (feature vectors) represent the frequencies with which certain events have been generated by a multinomial ( p 1...

Sperner's theorem, in discrete mathematics, describes the largest possible families of finite sets none of which contain any other sets in the family...

"dots and dividers") is a graphical aid for deriving certain combinatorial theorems. It can be used to solve a variety of counting problems, such as how many...

coefficients should not be confused with the multinomial coefficients that occur in the multinomial theorem. The value of multiset coefficients can be given...

obtained by collecting like terms, or alternatively, by applying the multinomial theorem. The special case f ( x ) = e x {\displaystyle f(x)=e^{x}} , g (...

(Y=m\mid Y\in \{1,m\}).\,} for m > 2. Different links g lead to multinomial logit or multinomial probit models. These are more general than the ordered response...

In statistics and econometrics, the multinomial probit model is a generalization of the probit model used when there are several possible categories that...

consequence of the Binomial theorem. The result about the numbers of degrees of freedom is valid when the original data are multinomial and hence the estimated...

doi:10.1214/aoms/1177728549. Mosimann, James E. (1962). "On the compound multinomial distribution, the multivariate β {\displaystyle \beta } distribution...

distribution is the conjugate prior of the categorical distribution and multinomial distribution. The infinite-dimensional generalization of the Dirichlet...

dog, lion, etc.), and the binary logistic regression generalized to multinomial logistic regression. If the multiple categories are ordered, one can...