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# Topic: Multinomial distribution

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 PlanetMath: multinomial distribution , the multinomial distribution is the same as the binomial distribution Cross-references: conditional probability, induction, distribution, multinomial, joint distribution, Poisson random variables, independent, binomial distribution, probability distribution function, vector, parameter, integer, fixed, random vector This is version 4 of multinomial distribution, born on 2004-08-26, modified 2006-10-02. www.planetmath.org /encyclopedia/MultinomialDistribution.html   (106 words)

 PlanetMath: multinomial distribution , the multinomial distribution is the same as the binomial distribution Cross-references: conditional probability, induction, distribution, multinomial, joint distribution, Poisson random variables, independent, binomial distribution, probability distribution function, vector, integer, fixed, random vector This is version 4 of multinomial distribution, born on 2004-08-26, modified 2006-10-02. planetmath.org /encyclopedia/MultinomialDistribution.html   (105 words)

 Multinomial PDF The multinomial distribution is a multivariate generalization of the binomial distribution. The binomial distribution is the probability of x successes in the n trials. The probability mass function for the multinomial distribution is defined as www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/multpdf.htm   (269 words)

 Multinomial distribution   (Site not responding. Last check: 2007-10-27) In probability theory, the multinomial distribution is a generalization of the binomial distribution. The binomial distribution is the probability distribution of the number of "successes" in n independent Bernoulli trials, with the same probability of "success" on each trial. The Dirichlet distribution is the conjugate prior of the Multinomial in Bayesian statistics. multinomial-distribution.mindbit.com   (179 words)

 Multinomial distribution - Wikipedia, the free encyclopedia In probability theory, the multinomial distribution is a generalization of the binomial distribution. The binomial distribution is the probability distribution of the number of "successes" in n independent Bernoulli trials, with the same probability of "success" on each trial. The Dirichlet distribution is the conjugate prior of the multinomial in Bayesian statistics. en.wikipedia.org /wiki/Multinomial_distribution   (339 words)

 PA 765: Logit, Probit, and Log-linear Models Where logistic regression is based on the assumption that the categorical dependent reflects an underlying qualitative variable and uses the binomial distribution, probit regression assumes the categorical dependent reflects an underlying quantitative variable and it uses the cumulative normal distribution. Multinomial distribution is assumed when sample size and row and/or column totals are predetermined (sampling has been stratified, for instance, in a race by religion table, the numbers of white Protestants, fl Catholics, etc., are predetermined). Multinomial logit handles non-independence by estimating the models for all outcomes simultaneously except, as in the use of dummy variables in regression, one category is "left out" to serve as a baseline. www2.chass.ncsu.edu /garson/pa765/logit.htm#multinomial   (14875 words)

 Multinomial Distribution: Probability Calculator It is the multinomial distribution for this experiment. In a multinomial experiment, the frequency of an outcome refers to the number of times that outcome occurs. A multinomial probability refers to the probability of obtaining a specified frequency in a multinomial experiment. stattrek.com /Tables/multinomial.aspx   (1023 words)

 Lecture 8—Wednesday, January 25, 2006 The notion of a mixing distribution is a completely general one and appears in a number of other situations. The gamma distribution is a continuous distribution that should be viewed as a viable alternative to the normal distribution whenever the data in question are heteroscedastic. The lognormal distribution is a continuous distribution that should be viewed as a viable alternative to the normal distribution whenever the data in question are heteroscedastic. www.unc.edu /courses/2006spring/ecol/145/001/docs/lectures/lecture8.htm   (2087 words)

 The multinomial distribution Before defining the multinomial distribution, the binomial distribution is discussed. The use of the distribution is explained with an example. As with the binomial distribution, we are interested in the variables counting the number of times each outcome has occurred, where in the binomial case one variable for counting was enough, here we need www.cs.kuleuven.ac.be /~raf/homepage/publications/phd/node38.html   (512 words)

 Estimating expected frequencies The probability distribution of data are known for any of three sampling plans that are most frequently used: the multinomial distribution, the Poisson distribution and the product multinomial distribution. Multinomial distribution is characteristic of surveys: the total number of cases is fixed in advance and subjects (or observations) are cross-classified according to their joint distribution on the variables. The product multinomial distribution is obtained when the number of cases for each category but the dependent variable is fixed. tecfa.unige.ch /~lemay/thesis/THX-Doctorat/node240.html   (215 words)

 Bayesian smoothing through text classification Estimation of sparse multinomial distributions is an important component of many statistical learning tasks, and is particularly relevant to natural language processing. Perhaps the simplest and most elegant method of estimating a multinomial distribution is a generalization of an approach originally taken by Laplace. In order to extend the Bayesian approach to sparse multinomial distributions, several authors have used the notion of maintaining uncertainty over the vocabulary from which observations are produced as well as their probabilities. nlp.stanford.edu /courses/cs224n/2001/gruffydd/smoothing.html   (3059 words)

 [No title] Due to the Dirichlet distribution being the conjugate prior to the multinomial distribution, the probability of the corpus is derived easily. LDA generates a corpus in three stages: it first chooses the length of the corpus from a Poisson distribution, then picks a latent variable Theta according to a Dirichlet distribution which it finally uses to pick a topic from a multinomial distribution and words from a multinomial distribution conditioned on the topic variable. And the joint distribution of a topic mixture theta, a set of N topics z, and a set of N words w is defined in Equation 2. www.cs.wisc.edu /~apirak/cs/cs838/reviews_score_15.html   (7493 words)

 ISE 162 Sec. 1, Class Notes, Class 6   (Site not responding. Last check: 2007-10-27) The cumulative distribution function, F, is not particularly useful for the discrete uniform distribution. There is a similar redundancy for the multinomial, because if you know how many outcomes there are for each of the first k-1 outcome types, you subtract from n to get the number in the last outcome type. The hypergeometric distribution is a model for an engineering process where the population is finite. www.engr.sjsu.edu /jgille/notes2006b06.html   (1872 words)

 6. Bivariate Rand. Vars. A discrete bivariate distribution represents the joint probability distribution of a pair of random variables. The marginal distribution of X can be found by summing across the rows of the joint probability density table, and the marginal distribution of Y can be found by summing down the columns of the joint probability density table. You can simulate multinomial random variables on a computer by dividing the interval [0,1] into k subintervals where k is the number of different possible outcomes. www.csus.edu /indiv/j/jgehrman/courses/stat50/bivariate/6bivarrvs.htm   (2045 words)

 Discrete Probability Distribution - MULTINOMIAL DISTRIBUTION The multinomial distribution is an extension of the binomial distribution involving joint probabilities. In this case, the multinomial distribution is the joint probability distribution of the set of random variables X The probability distribution for the number of each type of hit, as well as outs and walks, in n at-bats is modeled as follows: library.thinkquest.org /10030/6dpdmd.htm   (191 words)

 Stats: Testing multinomial proportions (November 9, 2004) A multinomial distribution is used when your outcome variable has more than two possible values. The hypothesis that you want to test is that probability is the same for two of the categories in the multinomial distribution. You can also use a large sample normal approximation to the multinomial distribution, but you have to account for the fact that two multinomial proportions are negatively correlated. www.childrens-mercy.org /stats/weblog2004/MultinomialProportions.asp   (581 words)

 Quadratic Forms in Weak Inverses Again, the convergence to a chi-square distribution stems from the convergence of the vector of counters to a multivariate normal. The asymptotic distribution is a chi-square independent of the transition matrix and initial probabilities of the chain. We have seen that a famous measure suited to samples from a multinomial distribution, the Pearson chi-square, can be generalized to work with samples from arbitrary asymptotic multivariate normal distributions. random.mat.sbg.ac.at /~ste/diss/node22.html   (844 words)

 Some notation As we noted in class, and looking at the histograms, the main aspect of the bootstrap distribution of the median is that it can take on very few values, in the case of the treatment group for instance, The simple bootstrap will always present this discrete characteristic even if we know the underlying distribution is continuous, there are ways to fix this and in many cases it won't matter but it is an important feature. As long as the statistic is somewhat a smooth function of the observations, we can see that discreteness of the boostrap distribution is not a problem. www-stat.stanford.edu /~susan/courses/s208/node11.html   (623 words)

 Dirichlet distribution The multinomial distribution is a discrete distribution which gives the probability of choosing a given collection of The Dirichlet distribution is the conjugate prior of the parameters of the multinomial distribution. The pdfs of the Dirichlet distribution with certain parameter values are shown in Figure A.2. www.cis.hut.fi /ahonkela/dippa/node95.html   (187 words)

 Multinomial theorem - Wikipedia, the free encyclopedia In mathematics, the multinomial theorem is an expression of a power of a sum in terms of powers of the addends. The binomial theorem and binomial coefficients are special cases, for m = 2, of the multinomial theorem and multinomial coefficients, respectively. This proof of the multinomial theorem uses the binomial theorem and induction on m. en.wikipedia.org /wiki/Multinomial_theorem   (200 words)

 [No title] In the multinomial model, each document is represented as a vector over the space of words, where each element in the vector indicates the frequency with which the word occurred in the document. Multinomial Model also takes Naive Bayes assumption:probability of a word in given document is indepent of its content and position. On the other hand, the second model, called multinomial model, represents a document as a multi-dimensional vector with each dimension corresponding to a word from the vocabulary and its value (ranging from 0 to the total number of words in the document) indicating the number of occurences of the word in the document. www.cs.wisc.edu /~apirak/cs/cs838/reviews_score_1.html   (4802 words)

 Lectures The marginal distribution of Y is not exhibited, it is the proportionality factor. Sometimes a prior distribution can be approximated by one that is in a convenient family of distributions, which combines with the likelihood to produce a posterior that is manageable. We see that an ``objective'' way of building priors for the binomial parameter was to use the `conjugate family' distribution that has the property that the updated distribution is in the same family. www-stat.stanford.edu /~susan/courses/s166/node2.html   (1942 words)

 Homework 8 The homework assigmnment also covers material on joint probability distributions, covariance and correlation (chapters 6). Joint Discrete Distribution: Describe what is meant by a joint distribution using everyday language. Multinomial Distribution: Recognize situations consistent with a multinomial distribution. courses.washington.edu /stats315/homework7.htm   (110 words)

 [No title]   (Site not responding. Last check: 2007-10-27) Sison and Glaz (1995) developed a method of constructing two-sided confidence intervals for multinomial proportions that is based on the doubly truncated Poisson distribution and their method performs well when the cell counts are fairly equally dispersed over a large number of categories. Introduction Confidence intervals for multinomial proportions can be constructed by relying on the usual large-sample methods when the cell counts are adequate (>5 per cell) so that coverage probabilities are at or near the nominal confidence level. Thus, ni (i = 1, , k) is the number of observations and pi = ni / n is the proportion observed in the ith cell of the k x 1 table (i = 1,... www.jstatsoft.org /v05/i06/Sisonfinal.doc   (1411 words)

 [No title] However, usually the repeated measurements are placed in separate columns in the data spreadsheet (i.e., each is a different variable); thus the index i (in the formulas for smaller-the-better, larger-the-better, and signed target) runs across the columns or variables in the data spreadsheet, or the levels of the factors in the outer array. Outliers are atypical (by definition), infrequent observations; data points which do not appear to follow the characteristic distribution of the rest of the data. This condition occurs frequently when fitting generalized linear models to categorical response variables, and the assumed distribution is binomial, multinomial, ordinal multinomial, or Poisson. www.statsoft.com /textbook/gloso.html   (1463 words)

 Multinomial distributions The simplest method to evaluate whether data really come from a multinomial distribution is to compare the observed count in each cell to the predicted count based on the modelled proportions, computing In this connection it must be remembered that when using Gadget, usually a huge number of observations are available so that the expected counts (which are of course estimated) are normally considered fixed. In practise this has been implemented using those length distributions which cut across several length classes and the modelled and observed length distributions have been aggregated into a fixed number (e.g. www.hafro.is /dst2/report2/node88.html   (396 words)

 Multinomial Distribution   (Site not responding. Last check: 2007-10-27) This is an extension of the binomial distribution to the case where there are more than two classes into which an event can fall. The most common example is a histogram containing N independent events distributed into n bins. Even though the events are independent, there is a correlation between bin contents because the sum is constrained to be N. rkb.home.cern.ch /rkb/AN16pp/node179.html   (106 words)

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