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Discrete probability distribution
statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete probability distribution that
Categorical_distribution
Variable capable of taking on a limited number of possible values
a categorical variable is referred to as a level. The probability distribution associated with a random categorical variable is called a categorical distribution
Categorical_variable
Distributions in probability theory
multinomial distribution. It reduces to the categorical distribution as a special case when n = 1. It also approximates the multinomial distribution arbitrarily
Dirichlet-multinomial distribution
Dirichlet-multinomial_distribution
Generalization of the binomial distribution
2 and n is 1, it is the categorical distribution. The term "multinoulli" is sometimes used for the categorical distribution to emphasize this four-way
Multinomial_distribution
Topics referred to by the same term
model theory Categorical data analysis Categorical distribution, a probability distribution Categorical logic, a branch of category theory within mathematics
Categorical
Statement regarding whether or not an item belongs to a category
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category
Categorical_proposition
Probability distribution
prior of the categorical distribution and multinomial distribution. The infinite-dimensional generalization of the Dirichlet distribution is the Dirichlet
Dirichlet_distribution
Statistical concept
K-dimensional random vector drawn from a Dirichlet distribution (the conjugate prior of the categorical distribution), and the parameters will be distributed according
Mixture_model
Particular case of the generalized extreme value distribution
plotting the distribution was made easier. In machine learning, the Gumbel distribution is sometimes employed to generate samples from the categorical distribution
Gumbel_distribution
Mathematical function for the probability a given outcome occurs in an experiment
replacement) Categorical distribution, for a single categorical outcome (e.g. yes/no/maybe in a survey); a generalization of the Bernoulli distribution Multinomial
Probability_distribution
Statistical Markov model
categorical distribution of the transition probabilities, is the Dirichlet distribution, which is the conjugate prior distribution of the categorical
Hidden_Markov_model
Probability distribution modeling a coin toss which need not be fair
{\textstyle \mathrm {Bernoulli} (p).} The categorical distribution is the generalization of the Bernoulli distribution for variables with any constant number
Bernoulli_distribution
t-distribution The Matrix Langevin distribution The matrix variate beta distribution The Uniform distribution on a Stiefel manifold The categorical distribution
List of probability distributions
List_of_probability_distributions
Probability distribution with more than one mode
and 2. Categorical, continuous, and discrete data can all form multimodal distributions. Among univariate analyses, multimodal distributions are commonly
Multimodal_distribution
Quantity in information theory
{\displaystyle p} . Without loss of generality, we can assume the categorical distribution is supported on the set [ N ] = { 1 , 2 , … , N } {\textstyle [N]=\left\{1
Information_content
Probability distribution
variable which achieves the minimum is distributed according to the categorical distribution Pr ( X k = min { X 1 , … , X n } ) = λ k λ 1 + ⋯ + λ n . {\displaystyle
Exponential_distribution
Probability distribution
… , p , {\displaystyle w_{i}\geq 0,i=1,\ldots ,p,} (defining a categorical distribution) it holds that ∑ j = 1 p w j X j Y j ∼ C a u c h y ( 0 , 1 ) .
Cauchy_distribution
Discrete-time stochastic process
label is drawn from the categorical p {\displaystyle \mathbf {p} } . Since the Dirichlet distribution is conjugate to the categorical, the hidden variable
Chinese_restaurant_process
Statistical modeling method
Bernoulli distribution/binomial distribution for binary choices, or a categorical distribution/multinomial distribution for multi-way choices), where there
Linear_regression
Probability distribution
machine learning, the continuous Bernoulli distribution is a family of continuous probability distributions parameterized by a single shape parameter λ
Continuous Bernoulli distribution
Continuous_Bernoulli_distribution
Central concept in Kantian moral philosophy
The categorical imperative (German: Kategorischer Imperativ) is the central philosophical concept in the deontological moral philosophy of Immanuel Kant
Categorical_imperative
Discrete-variable probability distribution
only a single trial (draw) this is a categorical distribution. An example of a multivariate discrete distribution, and of its probability mass function
Probability_mass_function
Class of statistical models
K possible values. For the multinomial distribution, and for the vector form of the categorical distribution, the expected values of the elements of
Generalized_linear_model
Mathematical methods used in Bayesian inference and machine learning
\alpha _{0}} . The Dirichlet distribution is the conjugate prior of the categorical distribution or multinomial distribution. W ( ) {\displaystyle {\mathcal
Variational_Bayesian_methods
analysis of categorical data, also known as data on the nominal scale and as categorical variables. Bowker's test of symmetry Categorical distribution, general
List of analyses of categorical data
List_of_analyses_of_categorical_data
Probability distribution
Bernoulli distributions in exactly the same way as the Dirichlet distribution is conjugate to the multinomial distribution and categorical distribution. The
Beta_distribution
Statistical technique for smoothing categorical data
recommender systems. Bayesian average Prediction by partial matching Categorical distribution C. D. Manning, P. Raghavan and H. Schütze (2008). Introduction
Additive_smoothing
Numerical parameter in probability theory
categorical distribution. The prior distribution for the parameters of the categorical distribution would likely be a symmetric Dirichlet distribution. However
Concentration_parameter
Distinction between nominal, ordinal, interval and ratio variables
(1990) described continuous counts, continuous ratios, count ratios, and categorical modes of data. See also Chrisman (1998), van den Berg (1991). Mosteller
Level_of_measurement
Family of probability distributions related to the normal distribution
chi-squared beta Dirichlet Bernoulli categorical Poisson Wishart inverse Wishart geometric A number of common distributions are exponential families, but only
Exponential_family
Family of stochastic processes
of the Dirichlet distribution. In the same way as the Dirichlet distribution is the conjugate prior for the categorical distribution, the Dirichlet process
Dirichlet_process
posterior distribution with prior 1 / 2 {\displaystyle 1/2} . For the general case the estimate is made using a Dirichlet-Categorical distribution. Rule of
Krichevsky–Trofimov_estimator
Generative topic model
that multinomial distribution here refers to the multinomial with only one trial, which is also known as the categorical distribution.) The lengths N i
Latent_Dirichlet_allocation
Branch of statistics
the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution can
Mathematical_statistics
Fourth standardized moment in statistics
'curved, arching') refers to the degree of tailedness in the probability distribution of a real-valued, random variable in probability theory and statistics
Kurtosis
Probability distribution
statistics, Student's t distribution (or simply the t distribution) t ν {\displaystyle t_{\nu }} is a continuous probability distribution that generalizes the
Student's_t-distribution
Smooth approximation of one-hot arg max
sample categorical distributions Partition function Exponential tilting – a generalization of Softmax to more general probability distributions Positive
Softmax_function
Type of logical argument that applies deductive reasoning
determining the distribution of each term in each statement, meaning whether all members of that term are accounted for. In categorical syllogisms, formal
Syllogism
Continuous probability distribution
probability theory and statistics, the Weibull distribution /ˈwaɪbʊl/ is a continuous probability distribution. It models a broad range of random variables
Weibull_distribution
Systematic classification of 12 related enumerative problems concerning two finite sets
distribution of N separate random variables, each with an X-fold categorical distribution. Sampling with replacement where ordering does not matter, however
Twelvefold_way
Ensenada – a census of part of Spain Categorical data Categorical distribution Categorical variable Cauchy distribution Cauchy–Schwarz inequality Causal Markov
List_of_statistics_articles
Deep neural network for generating raw audio
sample at a time. It does so by sampling from a softmax (i.e. categorical) distribution of a signal value that is encoded using μ-law companding transformation
WaveNet
Statistical hypothesis test
In simpler terms, this test is primarily used to examine whether two categorical variables (two dimensions of the contingency table) are independent in
Chi-squared_test
Continuous probability distribution
theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function
Logistic_distribution
Probability theory and statistics concept
are categorical variables, a conditional probability table is typically used to represent the conditional probability. The conditional distribution contrasts
Conditional probability distribution
Conditional_probability_distribution
Measure of local oscillation behavior
probabilities that the two probability distributions can assign to the same event. For a categorical distribution it is possible to write the total variation
Total_variation
Taxonomy of statistical data elements
data can have any of various types. Statistical data types include categorical (e.g. country), directional (angles or directions, e.g. wind measurements)
Statistical_data_type
Evaluates how likely it is that any difference between data sets arose by chance
is sampled IID from a categorical distribution C a t e g o r i c a l ( p 1 , . . . , p n ) {\displaystyle \mathrm {Categorical} (p_{1},...,p_{n})} over
Pearson's_chi-squared_test
Neural network that learns efficient data encoding in an unsupervised manner
The concrete autoencoder uses a continuous relaxation of the categorical distribution to allow gradients to pass through the feature selector layer,
Autoencoder
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
Number of occurrences in an experiment or study
distribution. In the case when n i = 0 {\displaystyle n_{i}=0} for certain i {\displaystyle i} , pseudocounts can be added. A frequency distribution shows
Frequency_(statistics)
Distribution of a country's total GDP amongst its population
In economics, income distribution covers how a country's total GDP is distributed amongst its population. Economic theory and economic policy have long
Income_distribution
Statistical test comparing two probability distributions
empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions
Kolmogorov–Smirnov_test
Type of data measuring one attribute
of data, the shape of the distribution of data and which measure of central tendency is being used. If the data is categorical, then there is no measure
Univariate_(statistics)
Numerical method
= 1 k ϕ j = 1 {\displaystyle \sum _{j=1}^{k}\phi _{j}=1} . See Categorical distribution. The following procedure can be used to estimate ϕ , μ , Σ {\displaystyle
EM_algorithm_and_GMM_model
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
Numerical measure of a statistical relationship between variables
variables followed a bivariate normal distribution. When both variables are dichotomous instead of ordered-categorical, the polychoric correlation coefficient
Correlation_coefficient
Statistical measure of how far values spread from their average
root of the variance. Technically, it is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often
Variance
Yi, for i = 1...n, of the outcomes of multi-way choices from a categorical distribution of size m (there are m possible choices). Along with each observation
Multinomial_probit
Concept in network science
tweak allocates vertices to communities randomly, according to a categorical distribution, rather than in a fixed partition. More significant variants include
Stochastic_block_model
Type of United States federal government funding to state and local projects
Categorical grants, also called conditional grants, are grants issued by the United States Congress which may be spent only for narrowly defined purposes
Categorical_grant
Measure of the asymmetry of random variables
theory and statistics is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Similarly to kurtosis
Skewness
Types of numerical variables in mathematics
statistical data types which are described with different probability distributions. A continuous variable is a variable such that there are possible values
Continuous or discrete variable
Continuous_or_discrete_variable
nominal. Nominal scale is also known as categorical. Interval scale is also known as numerical. When categorical data has only two possibilities, it is
List_of_statistical_tests
Psychometric model for analyzing categorical data
model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire
Rasch_model
Statistical model used in machine learning
{\displaystyle n} -way categorical distributions live; and where flows can be used to generalize e.g. Dirichlet, or uniform simplex distributions. As a first example
Flow-based_generative_model
Distribution of an uncertain quantity
A prior probability distribution (often simply called the prior probability, prior distribution, or prior) of an uncertain quantity is its assumed probability
Prior_probability
Conditional probability used in Bayesian statistics
updating. In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters
Posterior_probability
Probability distribution of the possible sample outcomes
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic. For an arbitrarily
Sampling_distribution
Monte Carlo algorithm
is a Dirichlet-multinomial distribution. The conditional distribution of a given categorical variable in this distribution, conditioned on the others
Gibbs_sampling
Variable representing a random phenomenon
elements of other sets E {\displaystyle E} , such as random Boolean values, categorical values, complex numbers, vectors, matrices, sequences, trees, sets, shapes
Random_variable
Statistical dispersion in nominal distributions
it. ANOSIM Categorical data Diversity index Fowlkes–Mallows index Goodman and Kruskal's gamma Information entropy Logarithmic distribution PERMANOVA Robinson–Foulds
Qualitative_variation
Concept in statistics
concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties
Shape of a probability distribution
Shape_of_a_probability_distribution
Table that displays the frequency of variables
visually. The relation between ordinal variables, or between ordinal and categorical variables, may also be represented in contingency tables, although such
Contingency_table
Type of statistical analysis
identical effects Cohen's kappa: measures inter-rater agreement for categorical items Friedman two-way analysis of variance (Repeated Measures) by ranks:
Nonparametric_statistics
Metric for fit of statistical models
Reduced chi-square The following are examples that arise in the context of categorical data. Pearson's chi-square test uses a measure of goodness of fit which
Goodness_of_fit
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation σ
Coefficient_of_variation
Type of chart
A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that
Bar_chart
Concept in statistics
category is a categorical variable. Categorical variables have two types of scales, ordinal and nominal. The first type of categorical scale is dependent
Nominal_category
Statistical model for a binary dependent variable
regression since about 1970. Binary variables can be generalized to categorical variables when there are more than two possible values (e.g. whether
Logistic_regression
Measure of variation in statistics
equations by the lowercase Greek letter σ (sigma). In the case of a normal distribution (as typified by the symmetrical bell-shaped curve), approximately 68
Standard_deviation
Statistical model for count data
tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a
Poisson_regression
Fundamental theorem in probability theory and statistics
appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution. This holds even if the original
Central_limit_theorem
Type of average of a collection of numbers
(values much larger or smaller than most others). For skewed distributions, such as the distribution of income for which a few people's incomes are substantially
Arithmetic_mean
Study of collection and analysis of data
science, in that dichotomous categorical variables may be represented with the Boolean data type, polytomous categorical variables with arbitrarily assigned
Statistics
transformation (if the distribution differs severely from normal) Make categorical (ordinal / dichotomous) (if the distribution differs severely from normal
Data_analysis
Quantum mechanics posed in terms of category theory
Categorical quantum mechanics is the study of quantum foundations and quantum information using paradigms from mathematics and computer science, notably
Categorical_quantum_mechanics
Probability distribution
noncentral t-distribution generalizes Student's t-distribution using a noncentrality parameter. Whereas the central probability distribution describes how
Noncentral_t-distribution
Probability distribution
normal distribution (GND) or generalized Gaussian distribution (GGD) is either of two parametric families of continuous probability distributions on the
Generalized normal distribution
Generalized_normal_distribution
Statistic measuring inter-rater agreement for categorical items
statistic used to measure inter-rater reliability for qualitative or categorical data. It is generally thought to be a more robust measure than simple
Cohen's_kappa
Value that appears most often in a set of data
normal distribution, but it may be very different in highly skewed distributions. The mode is not necessarily unique in a given discrete distribution since
Mode_(statistics)
Method used in statistics, pattern recognition, and other fields
linear combination of other features or measurements. However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant
Linear_discriminant_analysis
Statistics concept
variable is characterized statistically as an interaction; that is, a categorical (e.g., sex, ethnicity, class) or continuous (e.g., age, level of reward)
Moderation_(statistics)
Data whose unit can take on only two possible states
follow a binomial distribution, but when binary variables are not i.i.d., the distribution need not be binomial. Like categorical data, binary data can
Binary_data
Comparison of two distributions
of the quantiles of the second distribution (y-coordinate) plotted against the same quantile of the first distribution (x-coordinate). This defines a
Q–Q_plot
Test used in the analysis of stratified or matched categorical data
test (CMH) is a test used in the analysis of stratified or matched categorical data. It allows an investigator to test the association between a binary
Cochran–Mantel–Haenszel statistics
Cochran–Mantel–Haenszel_statistics
Model for generating observable data in probability and statistics
for classification. In machine learning, it typically models the joint distribution of inputs and outputs, such as P(X,Y), or it models how inputs are distributed
Generative_model
Function of the observed sample results
other nature, for instance, categorical (discrete) data, test statistics might be constructed whose null hypothesis distribution is based on normal approximations
P-value
Probability distribution
statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness
Skew_normal_distribution
Diagnostic plot of binary classifier ability
probability distributions for both true positive and false positive are known, the ROC curve is obtained as the cumulative distribution function (CDF
Receiver operating characteristic
Receiver_operating_characteristic
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CATEGORICAL DISTRIBUTION
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CATEGORICAL DISTRIBUTION
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