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Topic: Marginal distribution

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Julie Nixon Eisenhower

	Marginal distribution - Wikipedia, the free encyclopedia
		In probability theory, given two jointly distributed random variables X and Y, the marginal distribution of X is simply the probability distribution of X ignoring information about Y, typically calculated by summing or integrating the joint probability distribution over Y.
		Y = y) is the conditional distribution of X given Y.
		The marginals are obtained by summing the columns (or rows) -- the column sum would then be written in the margin of the table, ie.
	en.wikipedia.org /wiki/Marginal_distribution (212 words)

	PlanetMath: marginal distribution
		The most common marginal distribution is the individual marginal distribution (ie, the marginal distribution of ONE random variable).
		Cross-references: joint distribution, continuous, summing, subset, random variables
		This is version 5 of marginal distribution, born on 2001-10-26, modified 2004-06-09.
	planetmath.org /encyclopedia/MarginalDistribution.html (107 words)

	PlanetMath: marginal distribution
		This is, the marginal distribution of a set of random variables
		The most common marginal distribution is the individual marginal distribution (ie, the marginal distribution of ONE random variable).
		This is version 5 of marginal distribution, born on 2001-10-26, modified 2004-06-09.
	www.planetmath.org /encyclopedia/MarginalProbabilityFunction.html (108 words)

	Lecture 6—Monday, January 23, 2006
		From the way the row and column margins were defined, it is clear in Table 2 that the joint probabilities in each row when summed are equal to the row marginal probabilities, and the joint probabilities in each column when summed are equal to the column marginal probabilities.
		One distribution that satisfies all three requirements is the gamma distribution.
		The negative binomial error distribution then could still be used to account for the lingering heterogeneity that is not accounted for by the model.
	www.unc.edu /courses/2006spring/ecol/145/001/docs/lectures/lecture6.htm (1290 words)

	Forecast Verification Glossary
		A 2-dimensional histogram is a diagram plotting the marginal distribution of a variable in terms of its frequency of occurrence.
		The marginal distribution of the observations, p(x), is related to the uncertainty or base rate.
		marginal distribution, p(f), and can also be thought of as the degree to which probability forecasts approach categorical forecasts of 0 or 1.
	www.sec.noaa.gov /forecast_verification/Glossary.html (3068 words)

	Posterior Estimation - MCMC Integration
		The location of a marginal maximum and the mean is easy to verify, as is the appearance of the distribution, and probability statements are straight forward.
		If the marginal posterior of any one parameter is ill defined, then one or more of the other marginal posteriors might well be significantly shifted (biased); such interaction is often ignored in theory and practice.
		Marginal posteriors are based on the joint density sample of the next n points taken from (after) the burn point.
	www.sefsc.noaa.gov /HTMLdocs/synopsis.htm (2601 words)

	2
		The distribution division’s perceived marginal cost MC’ is therefore equal to its own marginal distribution cost MDC plus the internal price Pi that it must pay to buy the manufactured good.
		The perceived marginal cost MC’ of the distribution division is then equal to the sum of its own marginal distribution cost MDC plus the internal price Pe that it must pay to buy the manufactured good.
		The profit earned by the distribution division is then equal to the upper shaded area (yellow), while the manufacturing division earns the lower shaded area (blue).
	www.csun.edu /~hceco008/c11i.htm (1152 words)

	[No title]
		Example 3.5 The joint distribution function of X and Y is given by EMBED Equation.3 = 0 otherwise Find the joint density function and the marginal distribution functions of X and Y. 3.10 Important connections between the p.d.f ‘s and the joint c.d.f.’s.
		Solution Below is the joint or bivariate probability distribution of X and Y: X -2 -1012 Y100.090.150.270.250.04 200.01 0.050.080.050.01 From Example 3.2(a) the marginal distributions of X and Y are x -2-1012Total P(X =x) or EMBED Equation.3 0.10 0.20 0.35 0.30 0.05 1.00 y1020TotalP(Y = y) or EMBED Equation.3 0.80.201.00 Example 3.
		They are the means of the conditional distributions of X and Y. The mean of the conditional distribution of Y given X = x is denoted by EMBED Equation.3 The mean of the conditional distribution of X given Y = y is denoted by EMBED Equation.3.
	www.ecn.bris.ac.uk /www/ecdd/e12122/ch302.doc (1879 words)

	The Economics of Software Distribution over the Internet Revisited
		As distribution is such a crucial part of software production, further analysis of the mechanism that is used to distribute software over the Internet and the costs associated with such distribution is needed.
		Though sometimes referred to as "distribution" [2], the act of downloading by itself does not constitute an act of distribution, as it does not represent the act of bringing goods to a market where consumers can have access to it.
		The distributing vendor can only assess the scope of introduction generated when it has been realized, that is, when a software download has been made by a visiting consumer.
	www.firstmonday.org /issues/issue6_12/ilan/index.html (3898 words)

	The Bivariate Marginal Distribution Algorithm - Pelikan, Muhlenbein (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		The Bivariate Marginal Distribution Algorithm - Pelikan, Muhlenbein (ResearchIndex)
		BMDA is an extension of the Univariate Marginal Distribution Algorithm (UMDA).
		0.5: Marginal Distributions in Evolutionary Algorithms - Pelikan, Mühlenbein (1999)
	citeseer.ist.psu.edu /93545.html (352 words)

	The MathWorks - Demos - Simulation of dependent random variables using copulas
		The bivariate lognormal distribution is a simple solution in the case, and of course easily generalizes to higher dimensions and cases where the marginal distributions are _different_ lognormals.
		Other multivariate distributions also exist, for example, the multivariate t and the Dirichlet distributions are used to simulate dependent t and beta random variables, respectively.
		Compared to the bivariate Gamma/t distribution constructed earlier, which was based on a Gaussian copula, the distribution constructed here, based on a t(1) copula, has the same marginal distributions and the same rank correlation between variables, but a very different dependence structure.
	www.mathworks.com /products/demos/statistics/copulademo.html (2408 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.
		For example, the function f(x,y) = 1 when both x and y are in the interval [0,1] and zero otherwise, is a joint density function for a pair of random variables X and Y. The graph of the density function is shown next.
	www.csus.edu /indiv/j/jgehrman/courses/stat50/bivariate/6bivarrvs.htm (2045 words)

	Method for generating a correlated sequence of variates with desired marginal distribution for testing a model of a ...
		This method, to be described in more detail subsequently, uses as inputs an independent identically distributed random number stream of uniform marginals and a pair of specified control parameters, and subjects such inputs to a modulo 1 autoregressive scheme that yields a sequence of correlated variates with a uniform marginal distribution.
		When a desired non-uniform marginal probability distribution is desired, this derived sequence can be further modified to achieve the desired marginal probability distribution by use of standard distortion techniques.
		While the invention has been described with specific reference to providing a sequence of variates with desired marginal distribution and correlations for traffic studies, it should be evident that the basic principles should be applicable to providing such a sequence for comparable use in other applications.
	www.freepatentsonline.com /5257364.html (8042 words)

	No Title
		The marginal column distribution of the column variable summarizes the percentage of items having each of the possible values of that variable.
		distribution is equal to twice its degrees of freedom.
		The data are summarized in a two-way table with the columns referring to the populations and the rows to the categories of the response.
	www.math.montana.edu /~cherry/st217/notes/sec73 (1824 words)

	Network-level Metrics
		Plots of the bodies of marginal distributions help us to understand the most common fine-scale throughputs in a trace, while plots of the tails of marginal distributions explore the episodes of highest throughput in a trace.
		Figure 4.37 shows the marginal distribution of byte throughput in the inbound direction of the Leipzig-II trace, and the marginal distribution of the Poisson fit of this throughput process (depicted using a dashed line with white triangles).
		Each line in the envelope corresponds to a distribution constructed by sampling the theoretical normal distribution as many times as values were present in the empirical marginal distribution.
	www.cs.unc.edu /~fhernand/diss-html/node26.html (8133 words)

	Multivariate Normal Distribution
		Perhaps the simplest is this: A random vector has a joint-normal distribution if every non-trivial liner polynomial of the random vector is itself normal.
		Both components are marginally normal, but the random vector is not joint-normal.
		Johnson and Wichern (2002) is a multivariate statistics text with a full chapter on the joint-normal distribution.
	www.riskglossary.com /articles/joint_normal_distribution.htm (632 words)

	The Negative Binomial Distribution. As the marginal distribution of the Binomial
		The negative binomial distribution is also known as the Pascal Distribution or the Polya Distribution.
		The Geometric Distribution is a special case of the negative binomial distribution with the number positive, in the second blue box, being '1' (one).
		The negative binomial distribution does basically the same thing as the Binomial, except that now we are asking about the probability of a particular sample size, given that we have found 'x' results to be positive (or 'white', or 'car crashes'), whereas we had expected to find 'u' results to be positive.
	home.clara.net /sisa/negb2hlp.htm (350 words)

	DRAFT TESTIMONY IN SDG&E RATE DESIGN WINDOW (Site not responding. Last check: 2007-10-09)
		Thus, it is clear that the credits for RCS should reflect the utility’s marginal costs of providing these services and should not be different from the "marginal costs" that are used by the utility for ratemaking purposes.
		This lower customer-related allocation reflects that primary distribution is the main driver of these expenses, and that less money is spent to trim trees near service drops than their percentage of overhead plant.
		Distribution mapping expenses should be allocated based on property (24% customer) instead of as an overhead expense (49% customer per SDGandE, 47% per UCAN) to reflect the nature of the work done.
	www.ucan.org /law_policy/energydocs/RDWtest.html (6520 words)

	An Informal Introduction to Copulas
		We take the marginal distributions, each of which describes the way in which a random variable moves “on its own,” and the copula function tells us how they “come together” to determine the multivariate distribution.
		Elliptical distributions include the normal as a special case, and are attractive because they are less restrictive than the normal, but retain much of its attractiveness and tractability.
		In addition, even where correlations are defined, the marginal distributions and correlations do not suffice to determine the joint multivariate distribution, so correlation no longer tells us everything we need to know about dependence.
	www.fenews.com /fen36/topics_act_analysis/topics_act_analysis.html (1409 words)

	The Economics of Software Distribution over the Internet Revisited
		When we usually think of distribution we think of it in terms of mobilizing products from the location in which they are produced and stored to the market in which they are consumed (Ganeshan and Harrison, 1995).
		It can thus be argued that for software distributed over the Internet, the act of distribution does not mean mobilizing products from the location in which they are produced to the market, as is the case with traditional products, and neither does it mean the act of downloading such software.
		Because we regard distribution as an act of production, the model is describing the process of distribution within a distribution channel in a way that resembles the way production models describe production within a production facility.
	firstmonday.org /issues/issue6_12/ilan/index.html (3898 words)

	The Neoclassical Theory of Distribution
		So, in sum, the marginal productivity theorem of distribution says that if all factors are paid their marginal products, then the sum of factor incomes will add up to total product.
		"marginal productivity itself is not an objectively ascertained factor in the pricing problem, but is in fact one of the unknowns in the problem...[A factor's] marginal productivity, then, cannot be defined as anything other than [its] price, for this price represents precisely the contribution of the labour in question to the price of the product.
		They argued that when one re-defines the concept of marginal product in terms of loss, the definition which Carl Menger (1871) had used, then if all factors are paid their marginal product, it will not "add up".
	cepa.newschool.edu /het/essays/margrev/distrib.htm (9860 words)

	Household Synthesis Utility (Site not responding. Last check: 2007-10-09)
		It is certainly possible to derive the joint distribution of households from another source than the PUMS and it is possible to use another source for the marginal distribution of households than STF-3A.
		In a two dimensional STF-3A table, each column defines a marginal for an intersection of categories, i.e., a marginal for value A of classification variable X and value B of classification variable Y. In these, entries 3-N are left blank.
		A random drawing from a uniform distribution between 0 and 1, inclusive, is used in the household synthesizer to determine the vehicle ownership category of the household.
	www.urbansim.org /docs/data/dataprep/household_synthesis.xml (2470 words)

	Aggregation of Information Goods:
		A1: The marginal cost of producing copies of all information goods and the marginal distribution and transaction cost for all information goods are zero.
		For example, if the marginal cost of providing an additional component or servicing an additional user is c, then a seller who charges a fixed price p plus an additional price of c per component or user, will avoid the inefficiency of including too many components in the sale, or servicing too many users.
		Third, even when marginal costs are negligible and consumers are homogeneous, large aggregations of goods (or users) may be required to fully extract profits and to maximize efficiency.
	www.gsm.uci.edu /~bakos/aig/aig.html (7333 words)

	BioMed Central \| Full text \| A note on generalized Genome Scan Meta-Analysis statistics
		Koziol and Feng [2] provided an alternative derivation of the null distribution of the GSMA statistic via a combinatoric approach involving probability generating functions, and suggested an Edgeworth series approximation to its exact null distribution that improves upon the Wise [1] normal approximation.
		Wise [1] and Koziol and Feng [2] had investigated the marginal distribution of any of these (exchangeable) GSMA statistics, whereas under the order statistic formulation of Levinson [3], the joint distribution of the entire set of GSMA statistics is taken into account.
		The combinatorial argument utilized by Koziol and Feng [2] to derive the exact distribution of the unweighted GSMA statistic (which relies on probability generating functions) is generally no longer applicable in the weighted setting.
	www.biomedcentral.com /1471-2105/6/32 (2697 words)

	Marginal distribution - Definition, explanation
		In probability theory, given two jointly distributed random variables X and Y, the marginal distribution of X is simply the probability distribution of X ignoring information about Y, typically calculated by summing or integrating the joint probability distribution over Y.
		Y = y) is the conditional distribution of X given Y.
		The marginals are got by summing the columns (or rows) -- the column sum would then be written in the margin of the table, ie.
	www.calsky.com /lexikon/en/txt/m/ma/marginal_distribution.php (197 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		A conditional distribution is a distribution for one variable given a specific level of a second variable.
		Two marginal distributions can be created, one for Looks that will detail how important a student’s appearance is to their popularity regardless of the gender of the respondent, and one for Gender that will detail the percentage of males and females that responded regardless of their view of appearance on popularity.
		Creating Bar Graphs of Conditional Distributions To create bar graphs for the conditional distributions of Looks given Gender, you need to split the data so that you are only looking at one gender at a time.
	www.facstaff.bucknell.edu /jwright/Math217/216Labs/Lab8.doc (1041 words)

	[No title]
		3.3 Marginal probability distributions The marginal distributions are the distributions of X and Y considered separately and model how X and Y vary separately from each other.
		3.8 Marginal probability density function The marginal p.d.f of X is defined as EMBED Equation.3 and is the equation of a curve called the p.d.f.
		Integrating out to get the marginal density function of X gives EMBED Equation.3 EMBED Equation.3 In the integration which is with respect to y, x is treated as a constant.
	www.efm.bris.ac.uk /www/ecdd/e12122/ch302.doc (1879 words)

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