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Topic: Mean vector

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	Mean electrical axis
		The mean electrical axis is the average of all the instantaneous mean electrical vectors occurring sequentially during depolarization of the ventricles.
		This causes the septum to depolarize from left-to-right as depicted by vector 1.
		After another 20 milliseconds later, the mean vector is pointing toward the left arm and anterior chest as the free wall of the ventricle depolarizes from the endocardial to the epicardial surface (vector 3).
	www.cvphysiology.com /Arrhythmias/A016.htm (573 words)

	White noise - Wikipedia, the free encyclopedia
		I.e., it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix.
		To simulate an arbitrary random vector, we transform a white random vector with a carefully chosen matrix.
		We choose the transformation matrix so that the mean and covariance matrix of the transformed white random vector matches the mean and covariance matrix of the arbitrary random vector that we are simulating.
	en.wikipedia.org /wiki/White_noise (1350 words)

	Untitled Document
		An inverse measure of the vector dispersion described by the a95 is the precision parameter, k.
		The Fisherian distribution assumes that the vectors are equally spaced in azimuth around the mean and decrease in abundance away from the mean as is defined by the Fisherian probability distribution.
		This is a different vector distribution and the shape is defined on the basis of the degree of ellipticity.
	earth.usc.edu /~slund/tsa/vector-stats.html (649 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		A vector can generally be normalised by one of two useful criteria; one is to normalise such that the elements sum to a constant after normalisation, the other is to normalise such that the squares of the elements sum to a constant after normalisation.
		A (real-valued) unit vector is an example of a vector normalised according to the second criterion; the sum of the squares of the elements of a (real-valued) unit vector is 1.
		An data encoding vector or vector sequence (for the HMM case) from the training sequence is obtained, and processed using a known re-estimation procedure.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=03/83831.031009&ELEMENT_SET=DECL (8324 words)

	Rhythmicity of Spinal Neurons Activated During Each Form of Fictive Scratching in Spinal Turtles -- Berkowitz 86 (2): ...
		Mean vector length is plotted as a function of the depth (A and B), laterality (C), and spinal segment (D) of the recording.
		The mean vector angle is plotted on the circular axis; the radius of each point is the summary mean vector length and is an indication of the consistency of that phase preference across the segmental distribution of single units.
		The mean vector angle is plotted on the circular axis; the radius of each point is the summary mean vector length and is an indication of the consistency of that phase preference across each distribution of single units.
	jn.physiology.org /cgi/content/full/86/2/1026 (6624 words)

	[No title]
		This program uses the EM algorithm to estimate the maximum likelihood (ML) covariance matrix and mean vector in the presence of missing data.
		This is done by pre-multiplying the row`s pattern vector by its transpose and then performing element- wise multiplication of the swept matrix (actually, element- wise multiplication is performed on the swept matrix minus the nvar+1 row and column which hold the intercept terms).
		This vector is then post-multiplied by a column vector holding the regression parameters (the intercept term is concatenated to the vector of variable parameters).
	www.psych.yorku.ca /friendly/lab/files/macros/em_covar.sas (1400 words)

	Mean electrical vector
		This mean electrical vector represents the sum of all of the individual vectors at a given instant in time.
		The direction of this vector relative to the electrode axis determines, in part, the magnitude of the recorded potential as illustrated in the figure to the right (the mass of the tissue also determines amplitude - see ECG rules).
		When a mean vector is determined over time, for example, during the entire phase of depolarization of the myocardium, this is termed the mean electrical axis.
	www.cvphysiology.com /Arrhythmias/A015.htm (357 words)

	United States Patent Application: 0040181408
		This stream of feature vectors is provided to a decoder 412, which identifies a most likely sequence of words based on the stream of feature vectors, a lexicon 414, a language model 416 (for example, based on an N-gram, context-free grammars, or hybrids thereof), and the acoustic model 418.
		For example, if a gaussian mean is represented by the number 2, the codebook would indicate the mean of 1.40374 should be used, whereas if a gaussian variance is represented by the number 3, the codebook would indicate that the value of 0.0053 for the variance should be used.
		Generally, this includes calculating a mean and a variance for each centroid to represent a plurality of gaussian distributions wherein a total decrease in likelihood is minimized for the representation of the plurality of gaussian distributions.
	appft1.uspto.gov /netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PG01&p=1&u=/netahtml/PTO/srchnum.html&r=1&f=G&l=50&s1="20040181408".PGNR.&OS=DN/20040181408&RS=DN/20040181408 (6052 words)

	Multinormal
		For a bivariate normal distribution, there are five parameters: the mean of X, the mean of Y, the standard deviation of X, the standard deviation of Y and the covariance of X and Y. Remark.
		A = mean Wt - B*(mean Ht) = 165 - (4)(68) = 165-272 = -107,
		A difficulty with this method is that the presence of outliers fouls the estimation of the mean vector and covariance matrix.
	www.uic.edu /classes/idsc/ids470/jw4e/nts04.htm (1329 words)

	6.5.4.1. Mean Vector and Covariance Matrix
		The first step in analyzing multivariate data is computing the mean vector and the variance-covariance matrix.
		The mean vector consists of the means of each variable and the variance-covariance matrix consists of the variances of the variables along the main diagonal and the covariances between each pair of variables in the other matrix positions.
		The mean vector is often referred to as the centroid and the variance-covariance matrix as the dispersion or dispersion matrix.
	www.itl.nist.gov /div898/handbook/pmc/section5/pmc541.htm (172 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		While the mean vector is divided into three sub-vector sets in the present embodiment, it should be appreciated and understood by one skilled in the art that the teachings of the present invention are not limited to any particular number of sub-vector sets.
		The mean vector set (as well as the variance vector set) can be divided into other numbers of sub-vector sets, depending upon the particular applications and implementations of the present invention.
		for all the vectors in this cluster, denotes it as
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=02/29617.020411&ELEMENT_SET=DECL (4525 words)

	Using Hodographs
		Typically, the actual wind vectors are not drawn on the hodograph, but are indicated only by their endpoints on the polar coordinate chart.
		If the wind vectors on a hodograph represent the winds at even intervals (usually each kilometer or 500 m), the shear vectors are equivalent in terms of the depth they represent.
		Calculating the mean wind shear vector is simply a matter of averaging the x and y components of each of the single layer wind shear vectors.
	deved.comet.ucar.edu /mesoprim/hodograf/print.htm (2448 words)

	The effects of noise due to random undetected tilts and paleosecular variation on regional paleomagnetic directions
		Monte Carlo simulations were performed on two types of vector distributions: (1) distributions of vectors formed by perturbing a single orginal vector with a Fisher distribution of bedding poles (each defining a tilt correction) and (2) standard Fisher distributions.
		The Fisher mean direction of the distribution of vectors formed by perturbating a single vector with random undetected tilts is biased toward shallow inclinations, but this bias is insignificant for angular dispersions of bedding poles less than 20°.
		This observation implies that the mean pole calculated from a large set of paleomagnetic directions obtained for coeval rocks over a region will be effectively unbiased by random undetected tilts of those rocks provided the angular dispersion of the undetected tilts is less than about 20°.
	www.agu.org /pubs/crossref/1991/90JB02457.shtml (394 words)

	Vector
		Vectors keep track of their size, allowing you to construct algorithms which work with vectors of any length.
		Vectors can be passed (with a bit of know-how) to functions that accept arrays as arguments, so existing code written for arrays does not have to be rewritten.
		Since a vector stores elements in a single contiguous memory block, it would not be efficient to permit values to be inserted at anywhere but the end of a vector.
	www.mtsu.edu /~csjudy/STL/Vector.html (1338 words)

	Principal components analysis - Wikipedia, the free encyclopedia
		Assuming zero empirical mean (the empirical mean of the distribution has been subtracted away from the data set), the principal component w
		The original measurements are finally projected onto the reduced vector space.
		Subtract the empirical mean vector M from each column of the data matrix D.
	en.wikipedia.org /wiki/Principal_components_analysis (706 words)

	Expected Value (Expectation or Mean) (Site not responding. Last check: 2007-10-10)
		You might think of the mean of a distribution as being analogous to a center of mass.
		The means of each are indicated on the x-axes.
		In an engineering, a center of mass is a "balancing point." By visual inspection, you can confirm that the indicated means in Exhibit 1 appear to be "balancing points" for the two PDFs.
	www.riskglossary.com /articles/mean.htm (259 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		These are the mean direction (in degrees) the length of the resultant vector the vector strength or mean resultant length (length of resultant / number of observations) the circular range (length of smallest arc including all observations) (in degrees) Remarks ------- Suppose we have n measurements of a circular variable y.
		The default is 95, meaning that z is approximately 1.96.
		The resultant vector length, expressed in the units of the weights, is the vector strength * the mean weight.
	www.stata.com /users/njc/circstat/circsumm.hlp (368 words)

	Tables: Cond. Defects and Pre-excitation of the Ventricles
		Mean QRS vector directed as far as -30° to the left, and posteriorly as in left anterior-superior division block.
		Inferior infarction and pre-excitation of the ventricles are excluded as causes for abnormal leftward deviation of the mean QRS vector.
		It is sometimes difficult to determine the exact direction of the mean ST or T vectors and to calculate the ventricular gradient, limiting the use of analysis of the ST and T vectors and the ventricular gradient.
	www.aha.gr /Ventricular_electrocardiography/tab-VentElec.ch08.hurs-01.html (4185 words)

	Pressure - Wikipedia, the free encyclopedia
		It is a fundamental parameter in thermodynamics and it is conjugate to volume.
		Therefore, pressure is a scalar quantity, not a vector quantity.
		It is approximately equal to typical air pressure at earth mean sea level and is defined as follows.
	en.wikipedia.org /wiki/Pressure_(physics) (1193 words)

	Estimation of Parameters
		The parameters that must be estimated include the process mean vector, the process covariance matrix, and the control limit for the control chart.
		x1 vector of observations, and xbar is the mean vector of all observations.
		Once covariance matrices and mean vectors are estimated, it is important to estimate proper distribution of the statistic in order to determine appropriate control limits on the data set in question.
	www.sys.virginia.edu /mqc/index2c.html (939 words)

	CMBMCS (Site not responding. Last check: 2007-10-10)
		combines pairs of PCASYS mean vector and covariance matrix data files, to produce a mean/covariance pair that is approximately the same as would have resulted if all the vectors that were used to make the input means and covariances had been given to the meancov function in one large set.
		These covariances must all have the same order, which must be the second dimension of the input mean vector files.
		Its "number of vectors" field will be set to the sum of the values of that field across the input covariances.
	ffpis.sourceforge.net /man/cmbmcs.html (334 words)

	Research Projects
		Traditionally the unknown population mean is estimated by the sample mean.
		Unlike the sample mean, the preliminary test and shrinkage estimators can include both the sample data and the uncertain prior information for the estimation of the unknown parameters, like the population mean vector.
		Use of the approximate chi-square test statistic in the definition of the preliminary test estimator causes conflict in the biases and mean squared errors of the estimators.
	www.sci.usq.edu.au /staff/khans/projects.htm (1159 words)

	Jenness Enterprises - ArcView Extensions; Mahalanobis Distance Grids
		Mahalanobis surface grids require a set of independent variable data grids containing continuous numeric values, a vector of mean values for each independent variable, and a variance/covariance matrix for the set of independent variables.
		Users can use existing mean vector and covariance matrix tables if they have them available or they can generate them on-the-fly based on point locations distributed over the independent variable grids.
		We can use the points directly to generate a vector of mean slope and elevation values for these animal locations, plus a covariance matrix for both slope and elevation values.
	www.jennessent.com /arcview/mahalanobis_grids.htm (1756 words)

	IDL Help
		This version of MMM has been modified for UIT data to ; always use the mean value of the data when the mean is less than 5.
		The default is to ; return the mean when either (1) the mean is less than the ; median, or (2) the mean is under 5 E-units ; MODE - If this keyword is set, then UIT_MMM works exactly like MMM, ; i.e.
		The average ; and sigma are then recomputed and the process repeated up to 20 ; iterations: ; (2) The amount of contamination by stars is estimated by comparing the ; mean and median of the remaining sky pixels.
	www.astro.washington.edu /deutsch-bin/getpro/library37.html?UIT_MMM (645 words)

	MultinormalDistribution
		is a numerical value, vector, or matrix, and otherwise leaves the function in symbolic form.
		A standardized random vector has a zero mean vector and a covariance matrix equal to its correlation matrix.
		This is an inefficient means of computing 1000 multinormal variates because the Cholesky decomposition of the covariance matrix is computed for each variate.
	documents.wolfram.com /v5/Add-onsLinks/StandardPackages/Statistics/MultinormalDistribution.html (542 words)

	Multivariate Normal Distribution (Site not responding. Last check: 2007-10-10)
		During this period, there was a popular misperception that a sum of normal random variables is itself normal.
		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.
		Now let’s consider how a random vector might fail to be joint-normal despite each of its components being marginally normal.
	www.riskglossary.com /articles/joint_normal_distribution.htm (525 words)

	3482.2.8 Minimum Distance to Mean (Site not responding. Last check: 2007-10-10)
		The Minimum Distance To Mean method is a supervised classification method that first analyzes the training data you provide and calculates a mean vector for each prototype class, described by the class center coordinates in feature space.
		The Minimum Distance to Mean algorithm then determines the Euclidean distance from each unclassified cell to the mean vector for each prototype class and assigns the cell to the closest class.
		As the set of input vectors from a training set are fed repeatedly to the network, the back propagation algorithm adjusts the weights in each pass to minimize the squared error (difference between output and target values) over the training set.
	www.microimages.com /refman/xhtml/PROCE059.HTM (1850 words)

	Chapter 9: Hypothesis Testing for Fourier Coefficients
		A more general problem is to use repeated measures of a vector of Fourier coefficients to determine whether the mean vector is different from a given vector.
		The data vector and vector of complex Fourier coefficients for this dataset (D=11) are given in Table 9.1.
		Specifying the confidence region for the mean vector is harder.
	research.opt.indiana.edu /Library/FourierBook/ch09.html (2396 words)

	THEORY2: Decision Theory
		Samples from this type of distribution tend to cluster about the mean, and the extend to which they spread out depends on the variance.
		As with the univariate density, samples from a normal population tend to fall in a single cluster centered about the mean vector, and the shape of the cluster depends on the covariance matrix:
		The reason that the distance decreases slower in the x direction is because the variance for x is greater and thus a point that is far away in the x direction is not quite as distant from the mean as a point that is far away in the y direction.
	www.cs.mcgill.ca /~mcleish/644/normal.html (690 words)

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