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Topic: Multivariate random variable

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  Probability theory Encyclopedia   (Site not responding. Last check: 2007-10-14)
Probability theory is a branch of mathematics concerned with analysis of random phenomena.
The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion.
The theorem states that the average of many independent and identically distributed random variables tends towards a normal distribution irrespective of which distribution the original random variables follow.
www.hallencyclopedia.com /topic/Probability_theory.html   (1424 words)

  Multivariate random variable - Wikipedia, the free encyclopedia
A multivariate random variable or random vector is a vector X = (X
) whose components are scalar-valued random variables on the same probability space (Ω, P).
This measure is also known as the joint distribution of the random vector.
en.wikipedia.org /wiki/Multivariate_random_variable   (102 words)

A stochastic process is a random function, that is a random variable X defined on a probability space (Ω, Pr) with values in a space of functions F.
Stochastic processes may be defined in higher dimensions by attaching a multivariate random variable to each point in the index set, which is equivalent to using a multidimensional index set.
The particle is then viewed as being subject to a random force which, since the molecules are very small and very close together, is treated as being continuous and, since the particle is constrained to the surface of the liquid by surface tension, is at each point in time a vector parallel to the surface.
www.brainyencyclopedia.com /encyclopedia/s/st/stochastic_process.html   (1452 words)

 Kurtosis, Leptokurtosis and Platykurtosis
Kurtosis is a parameter that describes the shape of a random variable’s probability density function (PDF).
A normal random variable has a kurtosis of 3 irrespective of its mean or standard deviation.
If a random variable’s kurtosis is greater than 3, it is said to be leptokurtic.
www.riskglossary.com /articles/kurtosis.htm   (411 words)

 PlanetMath: non-central chi-squared random variable
The (central) chi-squared random variable is a special case of the non-central chi-squared random variable, when the non-centrality parameter
Cross-references: generalized inverse, rank, singular, covariance matrix, vector, random vector, property, chi-squared random variable, variance, mean, term, squares, sum, degrees, standard normal distribution, distribution, random variables, iid
This is version 2 of non-central chi-squared random variable, born on 2005-01-07, modified 2005-01-07.
planetmath.org /encyclopedia/NonCentralChiSquaredRandomVariable.html   (162 words)

 Stochastic Programming Bibliography (primary subject)
An upper bound on the expectation of simplical functions of multivariate random variables.
Convergence of a stochastic variable metric method with ap- plication in adaptive prediction.
Approximation theory for stochastic variational and ky fan inequalities in finite dimensions.
mally.eco.rug.nl /BIBLIO/SPPRIME.HTML   (7228 words)

 [No title]
K is dimension of the multivariate normal distribution.
SAMPLE = the number of times the multivariate normal random variable is sampled to generate the critical value.
RANDOM NUMBER GENERATION: This program doesn't reseed the GAUSS random number generator for large SAMPLE you may want to occasionally reseed the generator, so that random numbers don't cycle.
faculty.maxwell.syr.edu /whorrace/GAUSS/generaln.txt   (738 words)

 ISE 162 Sec. 1, Class Notes, Class 6   (Site not responding. Last check: 2007-10-14)
This is the pattern for transformations of random variables.
Notice that the values of the random variable don't have to be equally spaced or anything; all that matters is that the probability of each outcome is the same.
Each trial can be classified into one of k outcomes, with the random variable defined as the number of times that each of the k possibilities happens.
www.engr.sjsu.edu /jgille/notes2005b06.html   (1409 words)

 Random variables   (Site not responding. Last check: 2007-10-14)
Random variables are introduced for convenient description of experiments with numerical outcomes.
A random variable is the numerical quantity assigned to every outcome of the experiment.
Random variables that have the same probabilities are therefore considered equivalent.
math.uc.edu /~brycw/probab/books/smplbook/node23.html   (217 words)

 Highbeam Encyclopedia - Search Results for Random variable   (Site not responding. Last check: 2007-10-14)
Estimation and use of a multivariate parametric model for simulating heteroskedastic, correlated, nonnormal random variables: the case of Corn Belt corn, soybean, and wheat yields.
The benefits of random variable practice for spatial accuracy and error detection in a rapid aiming task.
An upper prediction limit for the arithmetic mean of a lognormal random variable.
www.encyclopedia.com /SearchResults.aspx?Q=Random+variable   (343 words)

 Earliest Known Uses of Some of the Words of Mathematics (R)
RANDOM DISTRIBUTION is found in 1854 in An Investigation of the Laws of Thought by George Boole: "If they have not, we may regard the phaenomenon of a double star as the accidental result of a 'random distribution' of stars over the celestial vault, i.e.
Random sampling was used by Karl Pearson in 1900 in the title, "On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling," Philosophical Magazine, 50, 157-175 (OED2).
Let A and B be two correlated organs (variables or measurable characteristics) in the same or different individuals, and let the sub-group of organs B, corresponding to a sub-group of A with a definite value a, be extracted.
members.aol.com /jeff570/r.html   (7582 words)

 Multivariate t Random Numbers
To generate an NxP matrix of t random numbers in Dataplot, you must specify a Px1 mean vector, a PxP variance-covariance matrix, and the desired degress of freedom (i.e., the shape parameter for the t distribution).
Dataplot first generates multivariate normal random numbers with a mean vector AMU and a variance-covariance matrix SIGMA using the RDMNOR routine.
As with univariate random numbers, the nultivariate normal random numbers are built on an underlying uniform random number generators.
www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/mvtran.htm   (508 words)

 INI Programme Managing Uncertainty Programme Report
· Multivariate regular variation is being developed as a broad general tool for understanding dependence in long-tailed time series.
what we can say about the values of a multivariate random variable conditional on the information that it lies in an extreme subset.
The mathematical analysis of multivariate regularly varying functions continues to develop, and has proved to be a valuable tool in developing statistical models for multivariate extremes.
www.newton.cam.ac.uk /reports/0102/muc.html   (1332 words)

The uniform distribution (random numbers): runif(n, min=, max=), the default value for min is 0 and max is 1, i.e., runif(n) will generate
Both of them are adjusted so that the errors have mean 0 and variance 1.
It is surprising it have such a large variation.
www.stat.ufl.edu /~yang/R/lesson4/lesson4.htm   (464 words)

 Multivariate Normal Random Numbers
For this reason, random numbers for multivariate distributions each have their own unique syntax.
Although you can generate P columns of normal random numbers, this does take into account any correlation between the variables (i.e., they are independent).
Dataplot generates multivariate normal random numbers with a mean vector AMU and a variance-covariance matrix SIGMA using the RDMNOR routine written by Charlie Reeves while he was a member of the NIST Statistical Engineering Division.
www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/mvnran.htm   (432 words)

 Probability for Double Major Students   (Site not responding. Last check: 2007-10-14)
Random variable, cumulative distribution function, density (when it exists), quantiles.
The distribution of a transformation of a univariate random variable.
The distribution of a transformation of a multivariate random variable.
www.math.tau.ac.il /~isaco/Prob_double.html   (215 words)

 A Statistical Model of the Aberration Structure of Normal, Well-Corrected Eyes
A statistical model of the wavefront aberration function of the normal, well-corrected eye was constructed based on normative data from 200 eyes which show that, apart from spherical aberration, the higher-order aberrations of the human eye tend to be randomly distributed about a mean value of zero.
, which allows for variation in the axial and lateral location of the pupil, which in turn allows for variation in the various reference axes of the eye and the magnitude of off-axis astigmatism.
The statistical structure of such a model is fully defined by the means and variances of the various Zernike modes and by the covariance between all possible pairs of modes.
research.opt.indiana.edu /Library/statModel/statModel.html   (2937 words)

 vu04-w20   (Site not responding. Last check: 2007-10-14)
We propose a sieve maximum likelihood (ML) estimation procedure for a broad class of semiparametric multivariate distribution models.
This class of models has gained popularity in diverse fields due to a) its flexibility in separately modeling the dependence structure and the marginal behaviors of a multivariate random variable, and b) its circumvention of the "curse of dimensionality" associated with purely nonparametric multivariate distributions.
We show that the plug-in sieve ML estimates of all smooth functionals, including the finite dimensional copula parameters and the unknown marginal distributions, are semiparametrically efficient; and that their asymptotic variances can be estimated consistently.
www.vanderbilt.edu /econ/wparchive/abstracts/vu04-w20.html   (199 words)

 GLLAMM Publications   (Site not responding. Last check: 2007-10-14)
Grilli, L. and Rampichini, C. A multivariate multilevel model for the analysis of graduates’ skills.
Finkelstein, M. A latent variable model for the analysis of variability in the classification of radiographs of pneumoconioses.
Dohoo, I.R., Tillard, E. and Stryhn, H. Linear and logistic multilevel models applied to evaluating sources of variation in components of the calving to conception interval of dairy cattle.
www.gllamm.org /pub.html   (3963 words)

 Functional projection pursuit   (Site not responding. Last check: 2007-10-14)
The classical multivariate technique of principal components analysis is a special case of EPP where the index of interestingness is simply the sample variance of the projection.
The reason for using a different index is to obtain superior view of the data, e.g.
Here the multivariate random variable X on K variables, say, is replaced by a random function (stochastic process) X(t).
www.maths.bris.ac.uk /research/stats/Postgrad/topics/nason.html   (493 words)

 Probability: Uniform Distribution
The U(a,b) distribution has constant probability density between a and b, and 0 probability density elsewhere.
A U(a,b) random variable has cumulative distribution function (CDF) and inverse CDF:
The expectation, standard deviation, skewness and kurtosis of a U(a,b) random variable are:
www.riskglossary.com /articles/uniform_distribution.htm   (218 words)

 Another Look at Principal Curves and Surfaces - Delicado (ResearchIndex)
Abstract: INTRODUCTION Consider a multivariate random variable X in R p with density function f and a random sample from X, namely X 1,..., X n.
273 Multivariate adaptive regression splines (context) - Friedman - 1991
6 On measuring internal dependence in a set of random variable..
citeseer.ist.psu.edu /470739.html   (753 words)

 Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
Energy Citations Database (ECD) Document #6663566 - Risk methodology for geologic disposal of radioactive waste: a distribution-free approach to inducing rank correlation among input variables for simulation studies
Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
Risk methodology for geologic disposal of radioactive waste: a distribution-free approach to inducing rank correlation among input variables for simulation studies
www.osti.gov /energycitations/product.biblio.jsp?osti_id=6663566   (134 words)

 EconPapers: Robustness of a semiparametric estimator of a copula
Abstract: Copulas offer a convenient way of modelling multivariate observations and capturing the intrinsic dependence between the components of a multivariate random variable.
An example involving the household expenditure data for Australia is used to compare and contrast the methods
Keywords: Copulas; multivariate joint distribution; inference function method; maximum likelihood mathod; semiparametric method (search for similar items in EconPapers)
econpapers.repec.org /paper/ecmausm04/317.htm   (316 words)

 Robustness of a semiparametric estimator of a copula
Copulas offer a convenient way of modelling multivariate observations and capturing the intrinsic dependence between the components of a multivariate random variable.
A semiparametric method for estimating the dependence parameters of copulas was proposed by Genest, Ghoudi and Rivest (1995), in which the marginal distributions are estimated nonparameterically by empirical distribution functions.
For technical questions regarding this item, or to correct its listing, contact: (Christopher F. Baum).
ideas.repec.org /p/ecm/ausm04/317.html   (377 words)

 PPI no. 1, 1980   (Site not responding. Last check: 2007-10-14)
On Calculation of Spectra of Stationary Random Processes on the Basis of Large Samples [View Abstract]
On Some Properties of One Class of Control Systems That Operate in Stationary Random Media [View Abstract]
On Bit Number Distribution upon Quantization of a Multivariate Random Variable [View Abstract]
www.ee.umd.edu /~abarg/ppi/contents/1-80.html   (111 words)

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