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Generalization of the binomial distribution
In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts
Multinomial_distribution
Topics referred to by the same term
Multinomial may refer to: Multinomial theorem, and the multinomial coefficient Multinomial distribution Multinomial logistic regression Multinomial test
Multinomial
Generalization of the binomial theorem to other polynomials
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_theorem
Regression for more than two discrete outcomes
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more
Multinomial logistic regression
Multinomial_logistic_regression
Distributions in probability theory
In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite
Dirichlet-multinomial distribution
Dirichlet-multinomial_distribution
Tree-based ensemble machine learning methods
proposed and evaluated as base estimators in random forests, in particular multinomial logistic regression and naive Bayes classifiers. In cases that the relationship
Random_forest
In statistics and econometrics, the multinomial probit model is a generalization of the probit model used when there are several possible categories that
Multinomial_probit
Multinomial test is the statistical test of the null hypothesis that the parameters of a multinomial distribution equal specified values; it is used for
Multinomial_test
Probabilistic classification algorithm
With a multinomial event model, samples (feature vectors) represent the frequencies with which certain events have been generated by a multinomial ( p 1
Naive_Bayes_classifier
Discrete probability distribution
the other hand, the categorical distribution is a special case of the multinomial distribution, in that it gives the probabilities of potential outcomes
Categorical_distribution
Class of statistical models
(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
Generalized_linear_model
Probability distribution
distribution is the conjugate prior of the categorical distribution and multinomial distribution. The infinite-dimensional generalization of the Dirichlet
Dirichlet_distribution
Statistical method
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Partial least squares regression
Partial_least_squares_regression
Probability distribution
In probability theory and statistics, the negative multinomial distribution is a generalization of the negative binomial distribution (NB(x0, p)) to more
Negative multinomial distribution
Negative_multinomial_distribution
Arrangement of trinomial coefficients
trinomial coefficients, expansions, and distributions are subsets of the multinomial constructs with the same names. Because the tetrahedron is a three-dimensional
Pascal's_pyramid
Choice between two or more discrete alternatives
many forms, including: Binary Logit, Binary Probit, Multinomial Logit, Conditional Logit, Multinomial Probit, Nested Logit, Generalized Extreme Value Models
Discrete_choice
Statistical model for a binary dependent variable
dog, lion, etc.), and the binary logistic regression generalized to multinomial logistic regression. If the multiple categories are ordered, one can
Logistic_regression
Regression model for ordinal dependent variables
making no assumptions of the interval distances between options. Multinomial logit Multinomial probit McCullagh, Peter (1980). "Regression Models for Ordinal
Ordered_logit
and 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
Proofs of Fermat's little theorem
Proofs_of_Fermat's_little_theorem
Probability multivariate distribution
In probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It
Dirichlet negative multinomial distribution
Dirichlet_negative_multinomial_distribution
Smooth approximation of one-hot arg max
generalization of the logistic function to multiple dimensions, and is used in multinomial logistic regression. The softmax function is often used as the last activation
Softmax_function
Moving average and polynomial regression method for smoothing data
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Local_regression
Generalized method of moments estimator in econometrics
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Arellano–Bond_estimator
Regression analysis for modeling ordinal data
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Ordinal_regression
Statistical model relating manifest and latent variables
and in latent profile analysis and latent class analysis as from a multinomial distribution. The manifest variables in factor analysis and latent profile
Latent_variable_model
Number of subsets of a given size
x {\displaystyle x} . Binomial coefficients can be generalized to multinomial coefficients defined to be the number: ( n k 1 , k 2 , … , k r ) = n
Binomial_coefficient
Describes the highest power of primes dividing a binomial coefficient
{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 {\tbinom
Kummer's_theorem
Branch of discrete mathematics
Gaussian binomial coefficient Multinomial generalizations Multinomial coefficient · Multinomial formula/theorem · Multinomial distribution · Pascal's pyramid
Combinatorics
Statistical model
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Random_effects_model
Discrete probability distribution
version of the Dirichlet-multinomial distribution as the binomial and beta distributions are univariate versions of the multinomial and Dirichlet distributions
Beta-binomial_distribution
Statistical modeling method
regression and probit regression for binary data. Multinomial logistic regression and multinomial probit regression for categorical data. Ordered logit
Linear_regression
Evaluates how likely it is that any difference between data sets arose by chance
i n o m i a l ( N ; 1 / 6 , . . . , 1 / 6 ) {\displaystyle \mathrm {Multinomial} (N;1/6,...,1/6)} , and χ 2 := ∑ i = 1 6 ( O i − N / 6 ) 2 N / 6 {\textstyle
Pearson's_chi-squared_test
restrictive assumption of mutually exclusive alternatives, which characterizes multinomial discrete choice methods. Ashford, J.R.; Sowden, R.R. (September 1970)
Multivariate_probit_model
estimation, simulation and diagnostic tools for multinomial discrete-choice models—ranging from basic multinomial logit to mixed logit, random-regret logit
NLOGIT
Regularization technique for ill-posed problems
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Ridge_regression
Method for model fitting in statistics
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Weighted_least_squares
Discrete probability distribution
{\displaystyle \{X=k\},} { Y i } {\displaystyle \{Y_{i}\}} follows a multinomial distribution, { Y i } ∣ ( X = k ) ∼ M u l t i n o m ( k , p i ) , {\displaystyle
Poisson_distribution
Theorem related to ordinary least squares
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Gauss–Markov_theorem
Experiment methodology
determine which of the variants is more effective. Multivariate testing or multinomial testing is similar to A/B testing but may test more than two versions
A/B_testing
Statistical regression technique
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Multilevel regression with poststratification
Multilevel_regression_with_poststratification
Probability distribution and special case of gamma distribution
binomial, and instead require 3 or more categories, which leads to the multinomial distribution. Just as de Moivre and Laplace sought for and found the
Chi-squared_distribution
Problem in machine learning and statistical classification
learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three
Multiclass_classification
Type of probabilistic logic
and can be represented as a Beta PDF (Probability Density Function). A multinomial opinion applies to a state variable of multiple possible values, and
Subjective_logic
Particular case of the generalized extreme value distribution
Gompertz function is obtained. In the latent variable formulation of the multinomial logit model — common in discrete choice theory — the errors of the latent
Gumbel_distribution
Constrained least squares problem
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Non-negative_least_squares
Type of statistical model
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Multilevel_model
Variable capable of taking on a limited number of possible values
analysis on categorical outcomes is accomplished through multinomial logistic regression, multinomial probit or a related type of discrete choice model. Categorical
Categorical_variable
Method for solving certain optimization problems
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Iteratively reweighted least squares
Iteratively_reweighted_least_squares
Family of probability distributions related to the normal distribution
fixed and known. For example: binomial (with fixed number of trials) multinomial (with fixed number of trials) negative binomial (with fixed number of
Exponential_family
Algebraic expansion of powers of a binomial
m ) {\displaystyle {\tbinom {n}{k_{1},\cdots ,k_{m}}}} are known as multinomial coefficients, and can be computed by the formula ( n k 1 , k 2 , … ,
Binomial_theorem
Mathematical function for the probability a given outcome occurs in an experiment
yes/no/maybe in a survey); a generalization of the Bernoulli distribution Multinomial distribution, for the number of each type of categorical outcome, given
Probability_distribution
Statistical model
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Mixed_logit
Free and open-source statistical program
score export to data functionality ✓ ✓ / AMOS X X Frequencies (Binomial, Multinomial, Contingency, Chi², log-linear regression) ✓ ✓ ✓ (✓) JAGS (Bayesian black-box
JASP
Statistical estimation technique
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Generalized_least_squares
Regression models accounting for possible errors in independent variables
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Errors-in-variables_model
analysis Multinomial distribution Multinomial logistic regression Multinomial logit – see Multinomial logistic regression Multinomial probit Multinomial test
List_of_statistics_articles
Statistical technique
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Total_least_squares
Statistical optimality criterion
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Least_absolute_deviations
Approximation method in statistics
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Non-linear_least_squares
Generating pseudo-random numbers that follow a probability distribution
distribution#Random variate generation Laplace distribution#Random variate generation Multinomial distribution#Random variate distribution Pareto distribution#Random variate
Non-uniform random variate generation
Non-uniform_random_variate_generation
Mathematical functions
that utilize standard hyperbolastic functions to model a dichotomous or multinomial outcome variable. The purpose of hyperbolastic regression is to predict
Hyperbolastic_functions
Probability distribution
also known as the logistic normal distribution, which often refers to a multinomial logit version (e.g.). A variable might be modeled as logit-normal if
Logit-normal_distribution
Statistical model
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Fixed_effects_model
Statistical technique
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Principal component regression
Principal_component_regression
representation of an integer Mahler's theorem Multinomial distribution Multinomial coefficient, Multinomial formula, Multinomial theorem Multiplicities of entries
List of factorial and binomial topics
List_of_factorial_and_binomial_topics
Indian statistician (1915–1996)
multivariate statistics, particularly for his measure of similarity between two multinomial distributions, known as the Bhattacharyya coefficient, based on which
Anil_Kumar_Bhattacharyya
Taiwanese environmental statistician
Quadrature Method in Inference Problems Arising From the Generalized Multinomial Distribution. After working for a year as a visiting assistant professor
Anne_Chao
t-distribution. The negative multinomial distribution, a generalization of the negative binomial distribution. The Dirichlet negative multinomial distribution, a generalization
List of probability distributions
List_of_probability_distributions
Board game
others (link) Kern, John C. (2006). "Pig Data and Bayesian Inference on Multinomial Probabilities". Journal of Statistics Education. 14 (3). American Statistical
Pass_the_Pigs
Regression algorithm
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Least-angle_regression
Formula in mathematics
k}={\frac {n!}{i!\,j!\,k!}}\,.} This formula is a special case of the multinomial formula for m = 3. The coefficients can be defined with a generalization
Trinomial_expansion
Statistical modeling technique
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Quantile_regression
Combinatorial identity about binomial coefficients
binomial coefficients. Pascal's rule can also be generalized to apply to multinomial coefficients. Pascal's rule has an intuitive combinatorial meaning, that
Pascal's_rule
Least squares approximation of linear functions to data
and differentiation — this is an application of polynomial fitting. Multinomials in more than one independent variable, including surface fitting Curve
Linear_least_squares
Dirichlet distribution (probability theory) Dirichlet-multinomial distribution Dirichlet negative multinomial distribution Generalized Dirichlet distribution
List of things named after Peter Gustav Lejeune Dirichlet
List_of_things_named_after_Peter_Gustav_Lejeune_Dirichlet
Concept in statistical mathematics
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Segmented_regression
Method for estimating the unknown parameters in a linear regression model
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Ordinary_least_squares
Survey-based statistical technique
marketing research practice has shifted towards choice-based models using multinomial logit, mixed versions of this model, and other refinements. Bayesian
Conjoint_analysis
Function in statistics
implementation is easier. Sigmoid function Discrete choice on binary logit, multinomial logit, conditional logit, nested logit, mixed logit, exploded logit,
Logit
Discrete-variable probability distribution
distribution (also known as the generalized Bernoulli distribution) and the multinomial distribution. If the discrete distribution has two or more categories
Probability_mass_function
Statistical technique for smoothing categorical data
x_{2},\ldots ,x_{d}\rangle } from a d {\displaystyle d} -dimensional multinomial distribution with N {\displaystyle N} trials, a "smoothed" version of
Additive_smoothing
Statistical estimation method
detailed example, refer to: Tetsuo Yai, Seiji Iwakura, Shigeru Morichi, Multinomial probit with structured covariance for route choice behavior, Transportation
Binary_regression
Visualization method
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
L-curve
Mathematical inequality explaining concentration of random variables
Bretagnolle–Huber–Carol Inequality bounds the difference between a vector of multinomially distributed random variables and a vector of expected values. A simple
Concentration_inequality
Type of mathematical expression
called a trinomial. A polynomial with two or more terms is also called a multinomial. A real polynomial is a polynomial with real coefficients. When it is
Polynomial
Taxonomy of statistical data elements
(specific blood type, political party, word, etc.) categorical multinomial logit, multinomial probit ordinal ordering categories or integer or real number
Statistical_data_type
Concept in statistics
Compounding a multinomial distribution with probability vector distributed according to a Dirichlet distribution yields a Dirichlet-multinomial distribution
Compound probability distribution
Compound_probability_distribution
Generative topic model
i , j ∼ Multinomial ( θ i ) . {\displaystyle z_{i,j}\sim \operatorname {Multinomial} (\theta _{i}).} (b) Choose a word w i , j ∼ Multinomial ( φ z
Latent_Dirichlet_allocation
choice models developed by Charles Manski in 1975. Unlike the multinomial probit and multinomial logit estimators, it makes no assumptions about the distribution
Maximum_score_estimator
Method of data analysis
Britain (PDF). Oxford Internet Institute. p. 6. Flood, Joe (2008). "Multinomial Analysis for Housing Careers Survey". Paper to the European Network for
Principal_component_analysis
Test of statistical significance
than two categories, and an exact test is required, the multinomial test, based on the multinomial distribution, must be used instead of the binomial test
Binomial_test
Statistical model containing both fixed effects and random effects
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Mixed_model
Principle in genetics
the probability of each diploid–diploid combination, which follows a multinomial distribution with k = 3. For example, the probability of the mating combination
Hardy–Weinberg_principle
Statistical model
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Fay–Herriot_model
Overview of and topical guide to machine learning
statistics Bayesian knowledge base Naive Bayes Gaussian Naive Bayes Multinomial Naive Bayes Averaged One-Dependence Estimators (AODE) Bayesian Belief
Outline_of_machine_learning
Distribution of new data marginalized over the posterior
three-parameter Student's t distribution, beta-binomial distribution and Dirichlet-multinomial distribution are all predictive distributions of exponential-family distributions
Posterior predictive distribution
Posterior_predictive_distribution
Points with no three in a line
Gijswijt's upper bound. Jiang showed that by precisely examining the multinomial coefficients that come out of Ellenberg and Gijswijt's proof, one can
Cap_set
Undirected, connected, and acyclic graph
with vertices 1, 2, …, n of degrees d1, d2, …, dn respectively, is the multinomial coefficient ( n − 2 d 1 − 1 , d 2 − 1 , … , d n − 1 ) . {\displaystyle
Tree_(graph_theory)
Similarity of two probability distributions
two non-normal distributions and illustrated this with the classical multinomial populations, this work despite being submitted for publication in 1941
Bhattacharyya_distance
Linear regression model with a single explanatory variable
regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Simple_linear_regression
MULTINOMIAL
MULTINOMIAL
MULTINOMIAL
MULTINOMIAL
Girl/Female
Arabic, Muslim
Fruit; Summer Fruit
Boy/Male
Muslim/Islamic
Meteor
Male
Yiddish
Yiddish form of Latin Benedictus, BENESH means "blessed."Â
Female
English
 Anglicized form of Greek Elisabet (Hebrew Eliysheba), ELISABETH means "God is my oath." In the Old Testament bible, this is the name of the wife of Aaron. In the New Testament, it is the name of the mother of John the Baptist. Compare with another form of Elisabeth.
Boy/Male
Tamil
Markhandeyan | மாரà¯à®•à®¾à®¨à¯à®¤à¯‡à®¯à®¨
Devotee of Lord Shiva
Boy/Male
Indian
Protractor, One who worships God
Boy/Male
Norse
Valuable; dear.
Girl/Female
Tamil
Garland
Girl/Female
American, Arabic, Australian, British, Chinese, Christian, Danish, English, French, German, Hebrew, Indian, Latin, Muslim, Polish, Romanian, Russian, Tamil
God is My Oath; Consecrated to God; Form of Elizabeth; Pledged to God; The Chosen; Unique; Precious
Female
English
Anglicized form of Danish Freya, FREA means "lady, mistress."
MULTINOMIAL
MULTINOMIAL
MULTINOMIAL
MULTINOMIAL
MULTINOMIAL
n. & a.
Same as Polynomial.