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gptkbp:instanceOf
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Probability distribution
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gptkbp:application
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gptkb:politics
Natural language processing
Genetics
Quality control
Survey analysis
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gptkbp:categoryCount
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k
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gptkbp:covariance
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Cov[Xi,Xj] = -n*pi*pj, i ≠ j
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gptkbp:describes
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Outcomes of n independent trials
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gptkbp:firstDescribed
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gptkb:Francis_Galton
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gptkbp:generalizes
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gptkb:Binomial_distribution
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gptkbp:hasSpecialCase
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Binomial distribution (k=2)
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https://www.w3.org/2000/01/rdf-schema#label
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Multinomial distribution
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gptkbp:meaning
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E[Xi] = n*pi
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gptkbp:outcomeType
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Categorical
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gptkbp:parameter
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Number of trials
Probability vector
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gptkbp:probabilityMassFunction
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P(X1=x1,...,Xk=xk) = n!/(x1!...xk!) * p1^x1 * ... * pk^xk
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gptkbp:probabilityVector
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(p1, ..., pk)
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gptkbp:relatedTo
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gptkb:Dirichlet_distribution
gptkb:Poisson_distribution
gptkb:Categorical_distribution
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gptkbp:sumOfProbabilities
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p1 + ... + pk = 1
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gptkbp:supports
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x1 + ... + xk = n, xi ≥ 0
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gptkbp:trialCount
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n
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gptkbp:usedIn
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gptkb:Monte_Carlo_methods
gptkb:simulation
gptkb:Game_theory
gptkb:Bag-of-words_model
gptkb:Contingency_tables
gptkb:Naive_Bayes_classifier
Ecology
Statistics
Epidemiology
Machine learning
Market research
Quality assurance
Polling
Document modeling
Genetic drift modeling
Genotype frequency modeling
Multinomial logistic regression
Multinomial test
Random sampling
Text classification
Topic modeling
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gptkbp:variant
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Var[Xi] = n*pi*(1-pi)
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gptkbp:bfsParent
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gptkb:Exponential_family
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gptkbp:bfsLayer
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6
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