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Distributions in probability theory
theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative
Dirichlet-multinomial distribution
Dirichlet-multinomial_distribution
Probability distribution
categorical distribution and multinomial distribution. The infinite-dimensional generalization of the Dirichlet distribution is the Dirichlet process. The
Dirichlet_distribution
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
Probability multivariate distribution
probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It is a
Dirichlet negative multinomial distribution
Dirichlet_negative_multinomial_distribution
Discrete probability distribution
It connects the categorical distribution with the related multinomial distribution. It shows why the Dirichlet distribution is the conjugate prior of the
Categorical_distribution
Discrete probability distribution
the Dirichlet-multinomial distribution as the binomial and beta distributions are univariate versions of the multinomial and Dirichlet distributions respectively
Beta-binomial_distribution
Monte Carlo algorithm
Dirichlet prior, and the joint distribution of these variables after collapsing is a Dirichlet-multinomial distribution. The conditional distribution
Gibbs_sampling
Generative topic model
the article on the Dirichlet-multinomial distribution, as part of a more general discussion of integrating Dirichlet distribution priors out of a Bayesian
Latent_Dirichlet_allocation
Probability distribution
theory and statistics, the negative multinomial distribution is a generalization of the negative binomial distribution (NB(x0, p)) to more than two outcomes
Negative multinomial distribution
Negative_multinomial_distribution
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
average 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
Distribution of new data marginalized over the posterior
beta-binomial distribution and Dirichlet-multinomial distribution are all predictive distributions of exponential-family distributions (the normal distribution, binomial
Posterior predictive distribution
Posterior_predictive_distribution
_{k+1}>q_{1}+\ldots +q_{k}} . The inverted Dirichlet distribution is conjugate to the negative multinomial distribution if a generalized form of odds ratio is
Inverted Dirichlet distribution
Inverted_Dirichlet_distribution
Probability distribution
In statistics, the generalized Dirichlet distribution (GD) is a generalization of the Dirichlet distribution with a more general covariance structure
Generalized Dirichlet distribution
Generalized_Dirichlet_distribution
Concept in statistics
beta distribution. Compounding a multinomial distribution with probability vector distributed according to a Dirichlet distribution yields a Dirichlet-multinomial
Compound probability distribution
Compound_probability_distribution
Mathematical function for the probability a given outcome occurs in an experiment
generalization of the binomial distribution Multivariate hypergeometric distribution, similar to the multinomial distribution, but using sampling without
Probability_distribution
t-distribution. The negative multinomial distribution, a generalization of the negative binomial distribution. The Dirichlet negative multinomial distribution
List of probability distributions
List_of_probability_distributions
Family of probability distributions related to the normal distribution
and Dirichlet-multinomial distributions. Other examples of distributions that are not exponential families are the F-distribution, Cauchy distribution, hypergeometric
Exponential_family
Mental exercise in probability and statistics
velocity distributions. The Ellsberg paradox. Balls into bins Coin-tossing problems Coupon collector's problem Dirichlet-multinomial distribution Noncentral
Urn_problem
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
If there are more items than boxes holding them, one box must contain at least two items
Combinatorial proof Dedekind-infinite set Dirichlet's approximation theorem Hilbert's paradox of the Grand Hotel Multinomial theorem Pochhammer symbol Ramsey's
Pigeonhole_principle
Graphical aid for deriving some concepts in combinatorics
binomial coefficient Partition (number theory) Twelvefold way Dirichlet-multinomial distribution Batterson, J. Competition Math for Middle School. Art of Problem
Stars and bars (combinatorics)
Stars_and_bars_(combinatorics)
Probability distribution
distributed. It is also known as the logistic normal distribution, which often refers to a multinomial logit version (e.g.). A variable might be modeled
Logit-normal_distribution
Random model in mathematics
binomial distribution: The distribution of number of white balls observed until a fixed number black balls are observed. Dirichlet-multinomial distribution (also
Pólya_urn_model
Statistical model relating manifest and latent variables
in latent profile analysis and latent class analysis as from a multinomial distribution. The manifest variables in factor analysis and latent profile analysis
Latent_variable_model
Type of probabilistic logic
Density Function). A multinomial opinion applies to a state variable of multiple possible values, and can be represented as a Dirichlet PDF (Probability Density
Subjective_logic
Compound probability distribution
\beta } red balls are observed. Negative binomial distribution Dirichlet negative multinomial distribution Johnson et al. (1993) Johnson, N.L.; Kotz, S.;
Beta negative binomial distribution
Beta_negative_binomial_distribution
Probability distribution used in multivariate hypothesis testing
Chi-squared distribution Dirichlet distribution F-distribution Gamma distribution Hotelling's T-squared distribution Student's t-distribution Wishart distribution
Wilks's_lambda_distribution
Direct relationship Directional statistics Dirichlet distribution Dirichlet-multinomial distribution Dirichlet process Disattenuation Discrepancy function
List_of_statistics_articles
Concept in probability theory
The same issues apply to the Dirichlet distribution. β is rate or inverse scale. In parameterization of gamma distribution,θ = 1/β and k = α. This is the
Conjugate_prior
Statistical concept
) given a fixed number of total occurrences Multinomial distribution, similar to the binomial distribution, but for counts of multi-way occurrences (e
Mixture_model
Theorem about independent random variables
result that is used when studying proportions, in particular the Dirichlet distribution. It is named after Eugene Lukacs. If Y1 and Y2 are non-degenerate
Lukacs's proportion-sum independence theorem
Lukacs's_proportion-sum_independence_theorem
Large-scale comparison of DNA sequences
(microsatellites, SNP-array genotyping, BayeScan (which uses the Dirichlet-multinomial distribution)) to place them into defined conservational units. This genomic
Population_genomics
Time-series clustering method
mixture of unobserved topics. Furthermore, each topic defines a multinomial distribution over a set of terms. Thus, for each word of each document, a topic
Dynamic_topic_model
Variable capable of taking on a limited number of possible values
multiple-category categorical variables are often analyzed using a multinomial distribution, which counts the frequency of each possible combination of numbers
Categorical_variable
Statistical technique for smoothing categorical data
\ldots ,x_{d}\rangle } from a d {\displaystyle d} -dimensional multinomial distribution with N {\displaystyle N} trials, a "smoothed" version of the counts
Additive_smoothing
Family of distributions that generalize the multivariate normal distribution
elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. In the simplified
Elliptical_distribution
Generating pseudo-random numbers that follow a probability distribution
generation Laplace distribution#Random variate generation Multinomial distribution#Random variate distribution Pareto distribution#Random variate generation
Non-uniform random variate generation
Non-uniform_random_variate_generation
Probability distribution
Laplace distributions are extensions of the Laplace distribution and the asymmetric Laplace distribution to multiple variables. The marginal distributions of
Multivariate Laplace distribution
Multivariate_Laplace_distribution
Formula in probability theory
The Dirichlet distribution is the conjugate prior for the multinomial distribution, which means that the posterior distribution is also a Dirichlet distribution
Rule_of_succession
Smooth approximation of one-hot arg max
probability distribution over K possible outcomes. It is a generalization of the logistic function to multiple dimensions, and is used in multinomial logistic
Softmax_function
Method for analyzing semantic data
each co-occurrence as a mixture of conditionally independent multinomial distributions: P ( w , d ) = ∑ c P ( d ) P ( c | d ) P ( w | c ) = P ( d ) ∑
Probabilistic latent semantic analysis
Probabilistic_latent_semantic_analysis
Evaluates how likely it is that any difference between data sets arose by chance
numbers are sampled from a multinomial distribution M u l t i n o m i a l ( N ; p 1 , . . . , p n ) {\displaystyle \mathrm {Multinomial} (N;p_{1},...,p_{n})}
Pearson's_chi-squared_test
a Dirichlet prior requires only adding the outcome frequencies to the Dirichlet prior alpha values, resulting in a Dirichlet posterior distribution for
Expected value of sample information
Expected_value_of_sample_information
Mathematical methods used in Bayesian inference and machine learning
{\displaystyle \alpha _{0}} . The Dirichlet distribution is the conjugate prior of the categorical distribution or multinomial distribution. W ( ) {\displaystyle
Variational_Bayesian_methods
Bayesian statistical inference method
(below), the Beta-binomial model, the Gaussian–Gaussian model, the Dirichlet-multinomial model, as well specific models for Bayesian linear regression (see
Empirical_Bayes_method
Concept in probability
3–57. J.-M. Bernard (2005). An introduction to the imprecise Dirichlet model for multinomial data. International Journal of Approximate Reasoning 39: 123–150
Probability_box
Mathematical function
definition of the Dirichlet distribution. Its relationship to the beta function is analogous to the relationship between multinomial coefficients and binomial
Beta_function
Type of sensitivity analysis
with distribution bands". Statistics and Decisions 13: 333–349. Bernard, J.-M. (2003). An introduction to the imprecise Dirichlet model for multinomial data
Robust_Bayesian_analysis
Commonly used representation of patterns in biological sequences
is 1. Each column can therefore be regarded as an independent multinomial distribution. This makes it easy to calculate the probability of a sequence
Position_weight_matrix
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
Concept in probability theory and statistics
multivariate hypergeometric, multivariate negative hypergeometric, multinomial, or Dirichlet distribution, but not in general otherwise. Formally, the partial correlation
Partial_correlation
Approximate interference technique in Bayesian networks
methods used by such techniques as latent Dirichlet allocation, and works by updating an approximate distribution at each node through messages in the node's
Variational_message_passing
Formula for the derivative of a product
derivative of an arbitrary number of factors, one has a similar formula with multinomial coefficients: ( ∏ i = 1 k f i ) ( n ) = ∑ j 1 + j 2 + ⋯ + j k = n ( n
Product_rule
Mathematical notation
{\alpha _{n}}{\beta _{n}}}={\frac {\alpha !}{\beta !(\alpha -\beta )!}}} Multinomial coefficient ( k α ) = k ! α 1 ! α 2 ! ⋯ α n ! = k ! α ! {\displaystyle
Multi-index_notation
Cell-free DNA profiling method
factors that can hinder the fragment length distribution sanity, Bayesian normalization via the Dirichlet-multinomial model should be done. Per every sample
EPIC-Seq
distributions / (1:C) Multinomial distribution / (F:D) Multivariate normal distribution / Gau Negative binomial distribution / (1:D) Pareto distribution / (1:C) Phase-type
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Automated recognition of patterns and regularities in data
empirical observations – using e.g., the Beta- (conjugate prior) and Dirichlet-distributions. The Bayesian approach facilitates a seamless intermixing between
Pattern_recognition
Probabilistic model
distributed according to a multinomial distribution conditional on a prior uniform draw … This prior is a special case of a Dirichlet distribution. v t e
Impartial_culture
Technique in natural language processing
while a Poisson distribution has been observed. Thus, a newer alternative is probabilistic latent semantic analysis, based on a multinomial model, which
Latent_semantic_analysis
Generalization of the product rule in calculus
k_{m}}={\frac {n!}{k_{1}!\,k_{2}!\cdots k_{m}!}}} are the multinomial coefficients. This is akin to the multinomial formula from algebra. The proof of the general
General_Leibniz_rule
Approximation of a function by a polynomial
}\end{aligned}}} where ( j α ) {\displaystyle {\tbinom {j}{\alpha }}} is the multinomial coefficient. Since 1 j ! ( j α ) = 1 α ! {\displaystyle {\tfrac {1}{j
Taylor's_theorem
Taiwanese mathematician alleged to have been murdered by KMT
Chen (1981-12-01). "Some local limit theorems in the symmetric Dirichlet-Multinomial urn models". Annals of the Institute of Statistical Mathematics
Chen_Wen-chen
Notion in calculus
more variables, an analogous expression holds, but with an appropriate multinomial expansion rather than binomial expansion. Higher order differentials
Differential_of_a_function
Generalized chain rule in calculus
obtained by collecting like terms, or alternatively, by applying the multinomial theorem. The special case f ( x ) = e x {\displaystyle f(x)=e^{x}} ,
Faà_di_Bruno's_formula
PMID 28584021. Nowicka M, Robinson MD (6 December 2016). "DRIMSeq: a Dirichlet-multinomial framework for multivariate count outcomes in genomics". F1000Research
List of RNA-Seq bioinformatics tools
List_of_RNA-Seq_bioinformatics_tools
DIRICHLET MULTINOMIAL-DISTRIBUTION
DIRICHLET MULTINOMIAL-DISTRIBUTION
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name from a place so called, perhaps Forshaw Heath in Solihull, Warwickshire, although the modern distribution is much further north.
Surname or Lastname
English
English : habitational name from a place named in Old English with hÄlig ‘holy’ + Old English feld ‘open country’. This may be Holyfield in Essex (which belonged to Waltham Abbey), but the present-day distribution of the name (mainly in the Midlands and Wales) suggests that another source may be involved.
Surname or Lastname
English
English : habitational name from Dearham in Cumbria or Dyrham in Gloucestershire, named from Old English dÄ“or ‘deer’ + hÄm ‘settlement’, ‘homestead’, or hamm ‘enclosure hemmed in by water’, ‘river meadow’. There are places in Norfolk called East and West Dereham, which have the same etymology. However, the present-day distribution of the surname suggests that they probably did not contribute to the surname.Irish (mainly Dublin, Drogheda, and Cork) : of English origin, but MacLysaght takes this to be a variant of Durham.
Surname or Lastname
English (Cambridge)
English (Cambridge) : unexplained; perhaps a habitational name from a lost or unidentified place. There are two places in England called Warland, in Durham and West Yorkshire, but the distribution of the modern surname suggests that a different souce is most probably involved.
Surname or Lastname
English (Lincolnshire)
English (Lincolnshire) : unexplained. Black identified this as a Scottish name of Pictish origin. However, the modern distribution of the surname, almost exclusively in Lincolnshire and adjoining counties, suggests a more localized eastern English origin.
Surname or Lastname
English (Devon)
English (Devon) : unexplained. Reaney and Wilson suggest that this may be from an Anglo-Scandinavian personal name Tukka, but the distribution in England makes a Scandinavian connection unlikely.
Surname or Lastname
English (West Yorkshire)
English (West Yorkshire) : topographic name for someone who lived in a long valley, from Middle English long + botme, bothem ‘valley bottom’. Given the surname’s present-day distribution, Longbottom in Luddenden Foot, West Yorkshire, may be the origin, but there are also two places called Long Bottom in Hampshire, two in Wiltshire, and Longbottom Farm in Somerset and in Wiltshire.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : apparently a habitational name from a lost or unidentified minor place in West Yorkshire, probably in the parish of Halifax, to judge by the distribution of early occurrences of the surname.
Surname or Lastname
English
English : habitational name for someone from a place called Elham, in Kent, or a lost place of this name in Crayford, Kent. The first is derived from Old English Ç£l ‘eel’ + hÄm ‘homestead’ or hamm ‘enclosure hemmed in by water’. There is also an Elam Grange in Bingley, West Yorkshire, but the current distribution of the name in the British Isles suggests that it did not contribute significantly to the surname.
Surname or Lastname
English
English : apparently a habitational name from places named Rushford in Devon, Norfolk, and Warwickshire. However, in view of the present-day distribution of the surname, a more likely source is Ryshworth in Bingley, West Yorkshire, which was earlier called Rushford (from Old English rysc ‘rushes’ + ford ‘ford’).
Surname or Lastname
English (chiefly West Midlands)
English (chiefly West Midlands) : habitational name from any of the various places so called, from Old English sūð ‘south’ + halh ‘nook’, ‘recess’. The distribution of the surname in Britain makes a Midlands origin likely: places called Southall in Doverdale, Worcestershire, and Billingsley, Shropshire, are possible sources.
Surname or Lastname
English
English : habitational name from places so called in North Yorkshire, Hampshire, and Kent. The Yorkshire place is named from the Old English personal name Hūna + tūn ‘enclosure’, ‘settlement’; that in Hampshire from the genitive plural of hund ‘hound’ + tūn ‘enclosure’, ‘settlement’; and the Kentish place from Old English huntena, genitive plural of hunta ‘hunter’ + dūn ‘hill’. The present-day distribution shows clusters in North and South Yorkshire, and also in Norfolk.
Surname or Lastname
English
English : habitational name from a place in Devon, recorded in Domesday Book as Loba, apparently a topographical term meaning perhaps ‘lump’, ‘hill’, the village being situated at the bottom of a hill. There is also a place of the same name in Oxfordshire (recorded in 1208 as Lobbe), but the historical and contemporary distribution of the surname (which is still largely restricted to Devon), makes it unlikely that it ever derived from this place, or from Middle English, Old English lobbe ‘spider’.
Surname or Lastname
English
English : habitational name from either of two places in Devon named Hunnacott, from either the Old English personal name HunÄ or Old English hunig ‘honey’ + cot ‘cottage’. There is also a place named Huncoat in Lancashire, which has the same origin, but the distribution of the surname in England suggests that it probably did not contribute to the surname.
Surname or Lastname
English
English : habitational name from places in Lancashire and Sussex. The former seems from the present-day distribution of the surname to be the major source, and is named from Old English scingel ‘shingle(s)’ + tūn ‘enclosure’, ‘settlement’; the latter gets its name from Old English sengel ‘burnt clearing’ + tūn.
Surname or Lastname
English
English : habitational name from any of various places named with this word: Hazleton Bottom (Hertfordshire), Hazleton Wood (Essex), or Hazelton (Gloucestershire), which is named from Old English hæsel ‘hazel’ + tūn ‘farmstead’, ‘settlement’. The present-day distribution of the surname points to the places in Essex and Gloucester as the likely sources.
Surname or Lastname
English
English : habitational name from the place in Bedfordshire (named in Old English as ‘settlement (Old English tūn) on the (river) Lea’), or, more plausibly in view of the pattern of distribution, from Luton in Devon (near Teignmouth), named in Old English as ‘Lēofgifu’s settlement’ (from an Old English female personal name composed of the elements lēof ‘dear’, ‘beloved’ + gifu ‘gift’). A further possible source of the name is Luton in Kent, named as the ‘settlement of Lēofa’.
Surname or Lastname
English
English : of uncertain derivation. The 18th-century parish registers of Marske, North Yorkshire, record the surname Hartburn with the variant Harburn; Harben may be a further variant of this. If so, its origin is probably topographic or habitational, from East Hartburn in Stockton-on-Tees or Hartburn in Northumberland, both named from Old English heorot ‘hart’ + burna ‘steam’. However, this conjecture is not borne out by the distribution of the surname a century later, when it occurs chiefly in Cambridgeshire and London and also with a significant presence in the Channel Islands, perhaps suggesting that it could be a variant of Harpin.
Surname or Lastname
English
English : habitational name from a place in West Yorkshire, probably named with the genitive case of the Old English personal name StÄn ‘stone’, a byname or short form of any of various compound names with this as the first element (compare, for example, Stammer, Stannard) + Old English feld ‘pasture’, ‘open country’.English : alternatively, it may be a topographic name from Middle English stanesfeld ‘open country of the (standing) stone’, with reference to a prominent monolith. There are other places so called, for example in Suffolk, but the distribution suggests that the one in Yorkshire is the source of the surname.
Surname or Lastname
English
English : of uncertain origin. Reaney suggests that it may be habitational name from Wincheap Street in Canterbury, but this origin is not supported by the present-day distribution of the surname, which is heavily concentrated in northeastern England.
DIRICHLET MULTINOMIAL-DISTRIBUTION
DIRICHLET MULTINOMIAL-DISTRIBUTION
Boy/Male
Indian, Punjabi, Sikh
Light of Lotus
Girl/Female
Arabic, Muslim
Morning
Female
Hebrew
(×¨Ö´× Ö¼Ö¸×”) Hebrew unisex name RINNAH means "shouting for joy." In the bible, this is the name of descendant of Judah. Although this is a masculine name in the bible, it is otherwise used primarily as a feminine name.
Boy/Male
Hindu, Indian, Marathi
Best of the Era
Girl/Female
Indian, Tamil
God Laxmi Name
Boy/Male
American, Anglo, Australian, British, Chinese, English, French
Fighter; Brave
Female
Russian
Variant spelling of Russian Zinoviya, ZINOVIA means "life of Zeus."Â
Girl/Female
Muslim
Male
Hindi/Indian
(रघà¥) Hindi name RAGHU means "swift."
Boy/Male
Australian, German, Italian, Spanish
Renowned in the Land; For; Form of Roland
DIRICHLET MULTINOMIAL-DISTRIBUTION
DIRICHLET MULTINOMIAL-DISTRIBUTION
DIRICHLET MULTINOMIAL-DISTRIBUTION
DIRICHLET MULTINOMIAL-DISTRIBUTION
DIRICHLET MULTINOMIAL-DISTRIBUTION
n.
A theory or system of social reform which contemplates a complete reconstruction of society, with a more just and equitable distribution of property and labor. In popular usage, the term is often employed to indicate any lawless, revolutionary social scheme. See Communism, Fourierism, Saint-Simonianism, forms of socialism.
n.
The act of distributing or dispensing; the act of dividing or apportioning among several or many; apportionment; as, the distribution of an estate among heirs or children.
n.
The law of likeness; similarity of structure; regularity in form and arrangement; orderly and similar distribution of parts, such that an animal may be divided into parts which are structurally symmetrical.
a.
Alt. of Multinominous
n.
An interior officer under the boatswain, gunner, or carpenters, charged with the stowage, account, and distribution of the stores.
n.
The arrangement or distribution of nerves, as in the leaves of a plant or the wings of an insect; nervation.
v. t.
To conjoin; to put together in distribution; to class.
n. & a.
Same as Polynomial.
a.
Of or pertaining to distribution.
n.
A notch cut crosswise in the shank of a type, to assist a compositor in placing it properly in the stick, and in distribution.
n.
A scheme for the distribution of prizes by lot or chance; esp., a gaming scheme in which one or more tickets bearing particular numbers draw prizes, and the rest of tickets are blanks. Fig. : An affair of chance.
n.
The study or description of the geographical distribution of animals.
n.
The branch of physical science which treats of the geographical distribution of rain.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
n.
A chart or graphic representation of the average distribution of rain over the surface of the earth.
n.
A place calculated for the rendezvous of troops, or for the distribution of them; also, a spot well adapted for offensive measures. Wilhelm (Mil. Dict.).
n.
That part of biology which relates to the animal kingdom, including the structure, embryology, evolution, classification, habits, and distribution of all animals, both living and extinct.
a.
Of or pertaining to rain; descriptive of the distribution of rain, or of rainy regions.
n.
The science of water, its properties, phenomena, and distribution over the earth's surface.
n.
Disposition; distribution; management.