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Topic: Random vector

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	PlanetMath: random vector (Site not responding. Last check: 2007-08-11)
		A random vector is a finite-dimensional formal vector of random variables.
		The random vector can be written either as a column or row of random variables, depending on its context and use.
		The size of a random vector and the size of a random matrix are assumed to be finite fixed constants.
	planetmath.org /encyclopedia/DistributionOfARandomMatrix.html (231 words)

	ometah: common/random.hpp File Reference
		Draw a random vector in a hyper sphere.
		Draw a random vector in a hyper sphere, using a biased method.
		Draw a random vector in a hyper cube.
	www.nongnu.org /ometah/doxygen/random_8hpp.html (387 words)

	Random Indexing of Linguistic Units for Vector-Based Semantic Analysis
		These index vectors would have a single 1 marking the place of the context (word or document) in a list of all contexts - the nth bit of the index vector for the nth document or word would be 1.
		The amount of noise we introduce by choosing random directions is so small that it does not have any noticeable effect on the similarity relations between the entries, which means that the local frequency matrix and the Random Indexing matrix contain approximately the same information.
		Furthermore, the high-dimensional sparse random index vectors may be used to cover basically any size of the vocabulary, without the need to increase the dimensionality of the vectors, which makes the technique extremely scalable.
	www.ercim.org /publication/Ercim_News/enw50/sahlgren.html (950 words)

	PlanetMath: joint normal distribution
		Like a random variable with a normal distribution, a finite set of random variables (or a random vector) with a joint normal distribution has some simple and attractive properties:
		any linear combination of random vectors that are jointly normal is jointly normal.
		be a random vector whose distribution is jointly normal.
	planetmath.org /encyclopedia/MultivariateGaussianDistribution.html (197 words)

	RANDOM
		RANDOM with no options causes a normal random variable with mean zero and variance one to be generated and stored as a series (under control of the current SMPL).
		To create a random variable from an empirical distribution function, a series (usually a set of residuals) generated by the distribution function must be supplied.
		All other random variables are derived from the uniform random variables using the inverse distribution function, which usually involves an asymptotic expansion (see the CDF references).
	www.tspintl.com /products/tsphelp/random.htm (1531 words)

	Multivariate random variable
		A multivariate random variable or random vector is a vector X=(X
		) whose components are random variables on the same probability space (Ω, P).
		This measure is also known as the joint distribution of the random vector.
	www.ebroadcast.com.au /lookup/encyclopedia/ra/Random_vector.html (59 words)

	multiple File 5
		To derive the statistical properties of OLS estimates, we must define the notion of a random vector along with the notion of the mean and variance of a random vector.
		For example the vector of disturbance terms is a random vector since each element of the vector is a random variable.
		A constant matrix is, of course, a special type of random matrix in the same sense that a constant is a special case of a random variable that does not vary across points in the sample space.
	qed.econ.queensu.ca /walras/custom/300/351B/notes/mul_05.htm (685 words)

	Speech coding method - Patent 5970444
		A speech coding method according to claim 14 in which the random codebook comprises a random codebook formed by a shape codebook formed by random signals or exciting vectors which define pulse positions and which are prepared by a learning process, and the polarities of the pulses, thus enabling 6.4 kbit/s speech coding.
		A pitch component vector candidate P is chosen from the plurality of pitch component vectors, and a random component vector candidate C is chosen from a plurality of fixed random component vectors (or random number vectors) contained in the random codebook 22.
		The gain controlled pitch component vector and random component vector from the gain part 38 are synthesized in the adder 32 to be fed to the synthesis filter 34 as exciting vectors, whereby a decoded speech is delivered.
	www.freepatentsonline.com /5970444.html (6544 words)

	Welcome to IT++!
		Observe that a declared vector (or matrix) is not cleared (the element values are undefined).
		Vector elements are numbered such that a(0) denotes the first element.
		Random vectors and matrices are easily obtained by using these predefined functions:
	itpp.sourceforge.net /latest/users_guide.html (1018 words)

	Random Perpendicular 3D Vector - GameDev.Net Discussion Forums
		It's possible that you generate a random vector that's parallel to the forward vector, in which case the velocity will be zero, but the odds are quite slim and in the worst case you have a particle with no sideways velocity.
		Any orthogonal vector is the cross-product of the forward vector and something else, and chances are that you spend more effort calculating it than you would crossing against a quasi-random vector.
		Vector random(rand(), rand(), rand()); Velocity = Cross(forward, random);
	www.gamedev.net /community/forums/topic.asp?topic_id=422884 (2278 words)

	Notation and Concepts
		Vectors are notated in bold letters and are assumed to be row vectors in general, column vectors are denoted by adding a prime like in
		If X is a random variable, we denote its expectation and variance by E[X] and V[X], respectively.
		The reader is assumed to be familiar with the concept of random vectors in
	random.mat.sbg.ac.at /~ste/diss/node4.html (154 words)

	vector<T, Alloc>
		is a Sequence that supports random access to elements, constant time insertion and removal of elements at the end, and linear time insertion and removal of elements at the beginning or in the middle.
		Defined in the standard header vector, and in the nonstandard backward-compatibility header vector.h.
		The vector's value type: the type of object that is stored in the vector.
	www.sgi.com /tech/stl/Vector.html (527 words)

	Random numbers
		As long as a random number is within the range of a random variable X, X is a valid model for x and x is a valid realization of X.
		The same is true for sequences of random numbers, since such sequences are simply realizations of a random vector describing an experiment yielding a vector of real numbers.
		As pointed out in the last section, the relation between the information expressed by random variables and random numbers can be used to motivate choosing the random variable describing a sequence of unlinked experiments to have the empirical distribution of that sequence.
	random.mat.sbg.ac.at /~ste/dipl/node9.html (910 words)

	Linear Polynomial of a Random Vector
		A linear polynomial of a random vector is a random variable defined as a linear polynomial of some random vector.
		These are general result for linear polynomials of random vectors.
		Suppose a random variable Z is equal to the sum of two other random variables A and B which are related by the functional relationship B = A
	riskglossary.com /articles/linear_polynomial_of_a_random_vecrtor.htm (445 words)

	Principal Component Analysis
		Principal component analysis can be performed on any random vector Z whose second moments exist, but it is most useful with multicollinear random vectors.
		Suppose a random variable reflects the time it takes for some event to occur, and if the random variable is measured in days, it has a standard deviation of 13.5.
		linear polynomial of a random vector A random variable or random vector that is defined as a linear polynomial of a random vector.
	www.riskglossary.com /articles/principal_components.htm (1554 words)

	r.random (Site not responding. Last check: 2007-08-11)
		The category values and corresponding category names already associated with the random vector point locations in the input map layer are assigned to these sites in the raster_output map layer.
		The user may specify the quantity of random locations to be generated either as a positive integer (e.g., 10), or as a percentage of the raster map layer's cells (e.g., 10%, or 3.05%).
		The user may provide program arguments on the command line, specifying an input map layer name (input=name), output raster map layer name (raster_output=name), output vector points map name (vector_output=name), and the number of sites to be randomly generated as a total number of sites (n=number) or as a percentage of the map's size (n=number%).
	grass.baylor.edu /grass60/manuals/html60_user/r.random.html (772 words)

	Random_Numbers
		The code for the calculation of the uniformly and normally-distributed random numbers was adapted from the code of the functions DUNI and DNOR in the package NMS.
		RANDOM_VECTOR returns a vector of uniformly-distributed random numbers whose length is given by the value of the argument N. If the argument NORMALIZE is present and has the value.TRUE., the vector will be normalized.
		If this argument is specified, a random vector will be returned which is in the subspace orthogonal to the subspace spanned by these vectors.
	www.psc.edu /biomed/dynamo/www_v2/Modules/random_numbers.html (172 words)

	Random Processes
		We can imagine a generalization of our previous ideas about random experiments so that the outcome of an experiment can be a 'Random Object', an example of which is a signal waveform chosen at random from a set of possible signal waveforms, which we term an Ensemble.
		An example of a Random Process X(t,α) is shown in figure 1, where t is time and α is an index to the various members of the ensemble.
		The members of the ensemble can be the result of different random events, such as different instances of the sound 'ah' during the course of this lecture.
	cnx.org /content/m11100/latest (424 words)

	NERSC Random Number Generators
		The random numbers are generated using the multiplicative congruential method with a user-specified seed.
		Chapter G05 of the NAG Parallel Library web documentation describes two routines for generating and manipulating random numbers that are unique to the NAG Parallel Library.
		Return a vector of random complex numbers from a uniform or normal distribution.
	www.nersc.gov /nusers/resources/software/libs/math/random (1562 words)

	White noise - Wikipedia, the free encyclopedia
		e., it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity 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.
		To whiten an arbitrary random vector, we transform it by a different carefully chosen matrix so that the output random vector is a white random vector.
	en.wikipedia.org /wiki/White_noise (1630 words)

	Random Number (Using Simulink) (Site not responding. Last check: 2007-08-11)
		By default, the sequence produced has a mean of 0 and a variance of 1, although you can vary these parameters.
		To generate a vector of random numbers with the same mean and variance, specify the Initial seed parameter as a vector.
		Avoid integrating a random signal because solvers are meant to integrate relatively smooth signals.
	www.phys.ufl.edu /docs/matlab/toolbox/simulink/ug/randomnumber.html (189 words)

	Generating random unit vectors in n-dimensional space (Site not responding. Last check: 2007-08-11)
		Steve Rayhawk pointed out that if you choose n numbers with a normal distribution, treat those as coordinates, and normalize the resulting vector into a unit vector, this chooses a uniformly distributed unit vector in n dimensions.
		The proof he supplied manipulated the formula for a normal distribution, showing that the product of n normal distributions is itself a normal distribution based on the distance of the point with those coordinates from the origin.
		The internal state is two vectors, x and y, which you have to initialize beforehand to be some unit vectors.
	burtleburtle.net /bob/rand/unitvec.html (549 words)

	Matrix Representation (Site not responding. Last check: 2007-08-11)
		Let an uppercase bold letter denote a vector of random variables (a random vector).
		Let the same letter written bold but lowercase denote the set of observations taken on the associated random vector.
		be the partitioned vector containing the observed-to-real transformed random variables from processes 1 through p.
	www.uwm.edu /People/haas/lomaptech/node9.html (86 words)

	NAMD: AVector Class Reference
		Copyright (c) 1995, 1996, 1997, 1998, 1999, 2000 by The Board of Trustees of the University of Illinois.
		00115 { 00116 //------------------------------------------------------ 00117 // divide this vector by divisor and return a ref to it 00118 //------------------------------------------------------ 00119 m_x /= divisor; 00120 m_y /= divisor; 00121 m_z /= divisor; 00122 return(*this); 00123 }
		00299 { 00300 //------------------------------------------------------------------- 00301 // scale this vector, whose (x,y,z) are in the range (0:1), 00302 // to be in the range (SmallVec:BigVec) 00303 //------------------------------------------------------------------- 00304 m_x = SmallVec.
	www.ks.uiuc.edu /Research/namd/doxygen/classAVector.html (801 words)

	Lab 1 - Review topics
		The magnetic field intensity - i – is a summation of a fixed trend (from the earth magnetic field) and a random signal due to random magnetic sources in the crust,
		The effect of the strong trend (the earth magnetic field) in the data will be modeled using a first order polynomial (y=ax+b); the coefficients of the polynomial a,b are unknown and to be estimated.
		Figure 1: Profile of the data and its modeling using a combination of a trend (y=ax+b) and random signal H×k.
	www.ferris.edu /htmls/academics/course.offerings/felusy/GS762/LAB6.htm (602 words)

	Nonlinear Solver Project: LOCA::Homotopy::Group Class Reference
		In certain instances we have seen the random vector force the solution to a set of variables that are unphysical and could break the function evaluations (cause them to return nan).
		The random vector can be modified to keep the values near the initial guess based on values supplied to the constructor of the HomotopyGroup:
		Certain second derivatives such as (Jn)_x are not calculated since only their action on vectors are needed for later solves.
	software.sandia.gov /nox/classLOCA_1_1Homotopy_1_1Group.html (1103 words)

	Class MakeRandomVector
		This class will create a vector of a specified length, and fill it with random integers.
		It is a sub-class of Algorithim, which means that the class is intended to be timed for efficiency.
		When instantiating the class, pass true as an argument to cause the class to pre-extend the vector.
	www.ecst.csuchico.edu /~kboorom/lab2/MakeRandomVector.html (179 words)

	ASPN : Python Cookbook : vector: A list based vector class supporting elementwise operations (Site not responding. Last check: 2007-08-11)
		This vector class stores elements in a list and hence allows the 'vector' to grow
		""" return hasattr(x,'__class__') and x.__class__ is vector def zeros(n): """ Returns a zero vector of length n.
		'vector' is really useful in conjunction with a corresponding
	aspn.activestate.com /ASPN/Cookbook/Python/Recipe/52272 (587 words)

	Random vector within range - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-08-11)
		i need to create a function that can create a random vector, within a certain range, to initialize a particle.
		once i find that random vector i just make that the velocity (speed and direction) of the particle.
		Posted - 6/11/2005 9:03:02 AM This thread was also about generating unit vectors, only this time the vectors were also allowed to point downwards (i.e.
	www.gamedev.net /community/forums/viewreply.asp?ID=2100426 (442 words)

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