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Topic: Gaussian distribution

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	Gauss, Johann Carl Friedrich Gauss - Famous mathematicians pictures, posters, gifts items, note cards, greeting cards, ...
		Overlying Gauss's portrait the Gaussian distribution curve is incised.
		This probability distribution curve is commonly referred to as the "normal distribution" by statisticians, and, because of its curved flaring shape, as the "bell curve" by social scientists.
		The Gaussian distribution has found wide application in numerous experimental situations, where it describes the deviations of repeated measurements from the mean.
	mathematicianspictures.com /Mathematicians/Gauss.htm (506 words)

	Normal distribution - Wikipedia, the free encyclopedia
		The normal distribution also arises in many areas of statistics: for example, the sampling distribution of the mean is approximately normal, even if the distribution of the population the sample is taken from is not normal.
		The normal distribution was first introduced by de Moivre in an article in 1733 (reprinted in the second edition of his The Doctrine of Chances, 1738) in the context of approximating certain binomial distributions for large n.
		The derivation of the maximum-likelihood estimator of the covariance matrix of a multivariate normal distribution is perhaps surprisingly subtle and elegant.
	en.wikipedia.org /wiki/Normal_distribution (4114 words)

	PROPHET StatGuide: Glossary (Site not responding. Last check: 2007-10-23)
		For discrete random variables, the distribution function is often given as the probability associated with each possible discrete value of the random variable; for instance, the distribution function for a fair coin is that the probability of heads is 0.5 and the probability of tails is 0.5.
		A heavy-tailed distribution is one in which the extreme portion of the distribution (the part farthest away from the median) spreads out further relative to the width of the center (middle 50%) of the distribution than is the case for the normal distribution.
		A light-tailed distribution is one in which the extreme portion of the distribution (the part farthest away from the median) spreads out less far relative to the width of the center (middle 50%) of the distribution than is the case for the normal distribution.
	www.basic.northwestern.edu /statguidefiles/sg_glos.html (7880 words)

	Multivariate normal distribution - Wikipedia, the free encyclopedia
		In probability theory and statistics, a multivariate normal distribution, also sometimes called a multivariate Gaussian distribution (in honor of Carl Friedrich Gauss, who was not the first to write about the normal distribution) is a specific probability distribution.
		The cumulative distribution function (cdf) F(x) is defined as the probability that all values in a random vector X are less than or equal to the corresponding values in vector x.
		Two random variables that are normally distributed may fail to be jointly normally distributed, i.e., the vector whose components they are may fail to have a multivariate normal distribution.
	www.wikipedia.org /wiki/Multivariate_Gaussian_distribution (825 words)

	Gaussian Distribution
		The Gaussian distribution is a continuous function which approximates the exact binomial distribution of events.
		The Gaussian distribution shown is normalized so that the sum over all values of x gives a probability of 1.
		The Gaussian distribution is also commonly called the "normal distribution" and is often described as a "bell-shaped curve".
	hyperphysics.phy-astr.gsu.edu /hbase/math/gaufcn.html (178 words)

	Normal distribution -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-23)
		The normal distribution, also called Gaussian distribution, is an extremely important (Click link for more info and facts about probability distribution) probability distribution in many fields, especially in (The science of matter and energy and their interactions) physics and (The discipline dealing with the art or science of applying scientific knowledge to practical problems) engineering.
		The normal distribution has the very important property that under certain conditions, the distribution of a sum of a large number of ((statistics) a variable whose values are independent of changes in the values of other variables) independent variables is approximately normal.
		A (A theoretical distribution that is a good approximation to the binomial distribution when the probability is small and the number of trials is large) Poisson distribution with parameter is approximately normal for large.
	www.absoluteastronomy.com /encyclopedia/n/no/normal_distribution.htm (4826 words)

	Normal distribution (Site not responding. Last check: 2007-10-23)
		That the distribution is called the normal or Gaussian distribution, instead of the de Moivrean distribution, is just an instance of Stigler's law of eponymy: "No scientific discovery is named after its original discoverer".
		The cumulative distribution function (hereafter cdf) is defined as the probability that a variable X has a value less than x, and it is expressed in terms of the density function as
		A binomial distribution with parameters n and p is approximately normal for large n and p not too close to 1 or 0.
	www.sciencedaily.com /encyclopedia/normal_distribution_1 (2283 words)

	Distributions (Site not responding. Last check: 2007-10-23)
		The Normal or Gaussian distribution plays a central role in statistics and has been found to be a very good model for many continuous distributions that occur in real situations.
		The exponential distribution is a special case of the gamma distribution where a=1 and B = 1/lambda.
		The probability distribution of a narrow band noise process n(t) was formulated by Rice in papers published in the Bell Laboratories Journal, 1944 and 1945.
	astronomy.swin.edu.au /~pbourke/analysis/distributions (901 words)

	Normal/Gaussian distribution
		N]) is random (stochastic), and whose distribution follows a Gaussian shape described by f(x) in equation 3.4.
		The Gaussian distribution function in Fig 3.2 gives a concise and approximate description of the Bergen September temperature range and likelihood of occurrence.
		Gaussian distribution is also commonly referred to as 'normal distribution'.
	www.gfi.uib.no /~nilsg/kurs/notes/node28.html (220 words)

	[No title]
		Distributions which conform to this equation are called Gaussian, or normal distributions.
		The Gaussian distribution is so common that much of the terminology of statistics and error analysis has been built upon it.
		But this distribution of means will have a smaller width than the width of the data distribution itself.
	www.lhup.edu /~dsimanek/scenario/errorman/distrib.htm (2370 words)

	Biostatistics for the Clinician Glossary
		A distribution or, more formally, a frequency distribution is simply a table, chart or graph which pairs each different value obtained from a sample or population with the number or proportion of times it occurs.
		Gaussian distributions are important to the clinician because they represent many situations where a condition is the result of a variety of factors summing together.
		The interquartile range of a distribution is one of the measures of variability of a distribution.
	www.uth.tmc.edu /uth_orgs/educ_dev/oser/LGLOS1_0.HTM (1915 words)

	PHYS-310 (Site not responding. Last check: 2007-10-23)
		The Gaussian function is evaluated by assuming that the mean is the same as that used in the Poisson function, and the standard deviation for the Gaussian function is just that obtained from the Poisson function, i.e., sqrt(mean).
		The Gaussian disctribution function is a continuous function of x, in contrast to the binomial distribution function or the Poisson distribution function in which cases, x is discrete only.
		Because the Gaussian distribution is a continuous, smooth function, you should plot it as a smooth curve (line) with no "data point" markers.
	physics.valpo.edu /courses/p310/assign_4.html (1771 words)

	1.3.6.6.1. Normal Distribution
		Since the general form of probability functions can be expressed in terms of the standard distribution, all subsequent formulas in this section are given for the standard form of the function.
		The location and scale parameters of the normal distribution can be estimated with the sample mean and sample standard deviation, respectively.
		The sampling distribution of the mean becomes approximately normal regardless of the distribution of the original variable.
	www.itl.nist.gov /div898/handbook/eda/section3/eda3661.htm (458 words)

	BioMed Central \| Full text \| Detecting outliers when fitting data with nonlinear regression - a new method based on ...
		Both distributions are part of a family of t distributions as shown in Figure 1.
		We simulated the scatter in 5000 experiments like this by generating Gaussian scatter with a standard deviation of 200, and adding a single outlier that was 1400 Y units away from the curve (shown as an open circle).
		In a Gaussian distribution, you expect 68.27% of the values to lie within one standard deviation of the mean.
	www.biomedcentral.com /1471-2105/7/123 (10401 words)

	Gaussian distribution: FAQ. D'Errico.
		The normal (or Gaussian) distribution is one which appears in an incredible variety of statistical applications.
		Even when the right conditions are not met however, the distributions found for many experimentally generated sets of data still tend to have a bell shaped curve that often looks quite like that of a normal.
		Even when a distribution may not be truly normal, it may still be convenient to assume that a normal distribution is a good approximation.
	www.pitt.edu /~wpilib/statfaq/gaussfaq.html (1510 words)

	Spatial Filters - Gaussian Smoothing
		The idea of Gaussian smoothing is to use this 2-D distribution as a `point-spread' function, and this is achieved by convolution.
		In theory, the Gaussian distribution is non-zero everywhere, which would require an infinitely large convolution kernel, but in practice it is effectively zero more than about three standard deviations from the mean, and so we can truncate the kernel at this point.
		The effect of Gaussian smoothing is to blur an image, in a similar fashion to the mean filter.
	homepages.inf.ed.ac.uk /rbf/HIPR2/gsmooth.htm (1121 words)

	GNU Scientific Library -- Reference Manual - Random Number Distributions (Site not responding. Last check: 2007-10-23)
		The cumulative distribution functions and their inverses are computed separately for the upper and lower tails of the distribution, allowing full accuracy to be retained for small results.
		For \alpha = 2 it is a Gaussian distribution with \sigma = \sqrt{2} c.
		, \theta_K) for a Dirichlet distribution with parameters
	www.gnu.org /software/gsl/manual/gsl-ref_19.html (3818 words)

	Binomial, Poisson and Gaussian distributions
		The Poisson distribution applies when you are counting the number of objects in a certain volume or the number of events in a certain time period.
		The Gaussian distribution applies when the outcome is expressed as a number that can have a fractional value.
		If you know the mean and SD of this distribution, you can compute the fraction of the population that is greater (or less) than any particular value.
	www.graphpad.com /quickcalcs/probability1.cfm (183 words)

	S Archive: Inverse Gaussian Distribution
		Density, cumulative probability, quantiles and random generation for the inverse Gaussian distribution.
		This is replicated to be the same length as p or q or the number of deviates generated.
		The inverse Gaussian is one of the response distributions used in generalized linear models.
	www.statsci.org /s/invgauss.html (184 words)

	The Bell-shaped, Normal, Gaussian Distribution
		For a normally distributed data set, the empirical rule states that 68% of the data elements are within one standard deviation of the mean, 95% are within two standard deviations, and 99.7% are within three standard deviations.
		Hence, if we accept the hypothesis that IQs are normally distributed, at least 99.85% of the population would have a lower IQ and less than 0.15% a higher one.
		Normal in statistics generally refers to the gaussian distribution or the "normal" way we would expect errors to be distributed.
	www.andrews.edu /%7Ecalkins/math/webtexts/stat06.htm (1287 words)

	The Prism Guide to Interpreting Statistical Results (Site not responding. Last check: 2007-10-23)
		The frequency distribution, or histogram, of the values is shown in the middle panel.
		The Gaussian distribution plays a central role in statistics because of a mathematical relationship known as the Central Limit Theorem.
		The central limit theorem says that if your samples are large enough, the distribution of means will follow a Gaussian distribution even if the population is not Gaussian.
	www.graphpad.com /articles/interpret/principles/gaussian.htm (360 words)

	GNU Scientific Library -- Reference Manual: The Gaussian Distribution (Site not responding. Last check: 2007-10-23)
		This function returns a Gaussian random variate, with mean zero and standard deviation
		The probability distribution for Gaussian random variates is,
		This function computes a gaussian random variate using the Kinderman-Monahan ratio method.
	linux.duke.edu /~mstenner/free-docs/gsl-ref-1.0/gsl-ref_268.html (140 words)

	Untitled Document - The Gaussian Distribution (Site not responding. Last check: 2007-10-23)
		Samples from the distributions described in this chapter can be obtained using any of the random number generators in the library as an underlying source of randomness.
		In the simplest cases a non-uniform distribution can be obtained analytically from the uniform distribution of a random number generator by applying an appropriate transformation.
		More complicated distributions are created by the acceptance-rejection method, which compares the desired distribution against a distribution which is similar and known analytically.
	www.ugcs.caltech.edu /info/gsl/randist_1.html (243 words)

	Gaussian Distribution with Specified Mean and Sigma
		QUESTION: I have to simulate noise in my experiment, so I want to create arrays with a normal (Gaussian) distribution of random numbers, but with a specific full width half maximum (FWHM) and mean.
		In IDL you can create an array of random numbers in a normal or Gaussian distribution, with a sigma of standard deviation of 1 with the RANDOMN function.
		So if you want a Gaussian distribution with a mean of 50 and a sigma of 3.5, the you simply do this:
	www.dfanning.com /math_tips/normsigma.html (165 words)

	Gauss his life works biography links pictures math genius 19th century mathematician astronomy drawing 17-gon or ...
		Gauss his life works biography links pictures math genius 19th century mathematician astronomy drawing 17-gon or polygon by ruler and compass only, gaussian distribution, celestial mechanics, astronomy, gaussian curvature, math research, physics, riemann hypothesis noneuclidean geometry, fundamental theorem of algebra, prime number theorem, quadratic reciprocity, complex numbers, property, california, florida
		He introduced gaussian gravitational constant, least squares method, normal (Gaussian) distribution.
		In 1818 his work on geodesy led to notion of curvature and he proved two surfaces are isometric if and only if there is a map between them which preserves curvature.
	www.gauss.info (361 words)

	The central limit theorem
		In fact, as we shall see, the Gaussian distribution is of crucial importance to statistical physics because, under certain circumstances, it applies to all systems.
		The central limit theorem guarantees that the probability distribution of any measurable quantity is Gaussian, provided that a sufficiently large number of statistically independent observations are made.
		We can, therefore, confidently predict that Gaussian distributions are going to crop up all over the place in statistical thermodynamics.
	farside.ph.utexas.edu /teaching/sm1/lectures/node21.html (330 words)

	Normal distribution
		It is common in processes for most measurements to cluster around a central value, with less and less measurements occurring further away from this center.
		For example, the distribution of holes across the target will gradually spread out from a central, most common placement, as below.
		The bell-shaped curve occurs surprisingly often and is consequently called a Normal distribution (or Gaussian distribution, after its discoverer, or simply Bell-curve) and has some very useful properties which can be used to help variation be understood and controlled.
	www.syque.com /improvement/Normal%20distribution.htm (85 words)

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