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	NationMaster - Encyclopedia: Gaussian binomial
		In mathematics, the Gaussian binomial (sometimes called the Gaussian coefficient, the q-binomial coefficient, or the Gaussian polynomial) is a q-analog of the binomial coefficients.
		Gaussian binomials occur in the counting of symmetric polynomial's and in the theory of partitions.
		In mathematics, the Gaussian binomials (sometimes called the Gaussian coefficients, or the q-binomial coefficients) are the q-analogs of the binomial coefficients.
	www.nationmaster.com /encyclopedia/Gaussian-binomial (303 words)

	Kids.Net.Au - Encyclopedia > Gaussian distribution (Site not responding. Last check: 2007-10-20)
		The normal or Gaussian distribution is a ubiquitous and extremely important probability distribution considered in statistics.
		It is actually a family of distributions of the same general form, differing only in their location and scale parameters: the mean and standard deviation.
		A binomial distribution with parameters n and p is approximately normal if n is big enough (the approximation is very good if both np and n(1-p) are at least 5).
	www.kids.net.au /encyclopedia-wiki/ga/Gaussian_distribution (1325 words)

	Gaussian binomial - Wikipedia, the free encyclopedia
		In mathematics, the Gaussian binomials (sometimes called the Gaussian coefficients, or the q-binomial coefficients) are the q-analogs of the binomial coefficients.
		The Pascal identities for the Gaussian binomials are
		Gaussian binomials occur in the counting of symmetric polynomials and in the theory of partitions.
	en.wikipedia.org /wiki/Gaussian_binomial (227 words)

	1.7 Distributions
		Some of the most important distributions are the Gaussian, the binomial and the Poisson distributions.
		The family of Gaussian distributions or bell curves (also known as normal distributions) is by far the most important set of distributions.
		A similar case would be encountered when counting the number of red cells that fall in a square on a hemocytometer grid, looking at the distribution of the number of individuals in America killed by lightening strikes in one year, or the occurrence of HIV associated needle sticks in US hospitals each year.
	www.uth.tmc.edu /uth_orgs/educ_dev/oser/L1_7.HTM (1067 words)

	Binomial coefficient - Definition, explanation
		In mathematics, particularly in combinatorics, the binomial coefficient of the natural number n and the integer k is defined to be the natural number
		The Catalan numbers have an easy formula involving binomial coefficients; they can be used to count various structures, such as treess and parenthesized expressions.
		This generalization is known as the generalized binomial coefficient and is used in the formulation of the binomial theorem and satisfies properties (3) and (7).
	www.calsky.com /lexikon/en/txt/b/bi/binomial_coefficient.php (834 words)

	List of topics named after Carl Friedrich Gauss - Wikipedia, the free encyclopedia
		Gaussian period, related to cyclotomy in number theory.
		Gauss' theorem may refer to the divergence theorem, which is also known as the Ostrogradsky-Gauss theorem.
		Gaussian distribution, also called the normal distribution, a type of probability distribution.
	en.wikipedia.org /wiki/Gaussian (157 words)

	Gaussian binomial (Site not responding. Last check: 2007-10-20)
		The Pascal identities for the Gaussian binomials are
		Like the ordinary binomial coefficients, the Gaussian binomials are center-symmetric i.e.
		and the invariance of the Gaussian binomials under the reflection
	www.wozhidao.org /en/Q-binomial.htm (242 words)

	Generalized Linear Models Theory
		For the binomial, multinomial, and Poisson distribution, terms involving binomial coefficients or factorials of the observed counts are dropped from the computation of the log-likelihood function since they do not affect parameter estimates or their estimated covariances.
		Overdispersion is a phenomenon that sometimes occurs in data that are modeled with the binomial or Poisson distributions.
		The function obtained by dividing a log-likelihood function for the binomial or Poisson distribution by a dispersion parameter is not a legitimate log-likelihood function.
	www.jmu.edu /docs/sasdoc/sashtml/stat/chap29/sect27.htm (1713 words)

	Binomial coefficient - Information from Reference.com
		In mathematics, particularly in combinatorics, the binomial coefficient of the natural number n and the integer k is the number of combinations that exist.
		Another name for the binomial coefficient is choose function; the binomial coefficient of n and k is often read as "n choose k".
		The formula for the binomial series was etched onto Newton's gravestone in Westminster Abbey in 1727.
	www.reference.com /search?q=Binomial+coefficient (1990 words)

	Definition of binomial name
		13: The [[multiplicationproduct]] of a binomial ''a + b'' with a factor ''c'' is obtain by [[dist...
		The binomial coefficient of ''n'' and ''k'' is also written as...
		1:...aussian polynomial''') is a [[q-analog]] of the [[binomial coefficients]].
	www.wordiq.com /search/binomial+name.html (963 words)

	Binomial, Poisson and Gaussian distributions
		The binomial distribution applies when there are two possible outcomes.
		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.
	graphpad.com /quickcalcs/probability1.cfm (183 words)

	PlanetMath: logistic regression
		is a binary response variable, so it has a binomial distribution with parameter (probability of success)
		random variables is simply the product of the individual binomial distributions.
		Comparing model equation for the logistic regression to that of the normal or Gaussian linear regression model, we see that the difference is in the choice of link function.
	www.planetmath.org /encyclopedia/Logit.html (450 words)

	Random Numbers
		Binomial distributions are associated with the probability of measuring a specific number of results given two possible values.
		The exponential and Gaussian distributions can be obtained through a change of variables.
		Thus, if we generate two uniform deviates, one associated with the Gaussian function of the radius vector and one associated with the angle, then the resulting distributions for x and y will have a Gaussian distribution.
	physics.tamuk.edu /~suson/html/4390/Random.html (2058 words)

	variable blur 0.4: a gaussian/binomial/average variable radius blur - Doom9's Forum
		Variableblur is a gaussian, binomial or average blur filter with a variable radius(variance).
		The binomial filter part is based on a paper by Frederick M. Waltz and John W. Miller.
		With radius = 2 it's closest to a gaussian blur with SD=1 and with radius=7 it's closest to SD=2.
	forum.doom9.org /showthread.php?t=88645 (1211 words)

	Open Channel Foundation: BPP
		The Binomial Probability program (BPP) is a menu driven program which performs a variety of functions related to the success/ failure situation.
		Other program capabilities are the calculation of probabilities from input data, Gaussian approximation, and the generation of a mean time between failure (MTBF) table for various levels of confidence.
		It is assumed that the user is familiar with the theory behind binomial probability distribution.
	www.openchannelfoundation.org /projects/BPP (237 words)

	Randomized Quantile Residuals
		Quantile residuals are based on the idea of inverting the estimated distribution function for each observation to obtain exactly standard normal residuals.
		In the case of discrete distributions, such as the binomial and Poisson, some randomization is introduced to produce continuous normal residuals.
		Quantile residuals are the only useful residuals for binomial or Poisson data when the response takes on only a small number of distinct values.
	www.statsci.org /s/qres.html (215 words)

	Gaussian Distribution (Site not responding. Last check: 2007-10-20)
		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 mean value is a=np where n is the number of events and p the probability of any integer value of x (this expression carries over from the binomial distribution).
	hyperphysics.phy-astr.gsu.edu /hbase/math/gaufcn.html (178 words)

	The fitness and structure of evolved libraries
		As for the shape-space model, the evolved libraries attain a fitness that has a similar functional dependency on the library size as the random libraries.
		The dependency is sublogarithmic, that is, the fitness increases slower than linear as a function of the logarithm of the library size.
		The shape-space model, with a binomial distribution of bond strengths, is well approximated by the Gaussian distributed bond strengths, as we expected.
	www.santafe.edu /~mihaela/thesis/node18.html (291 words)

	S 4.3 The Gaussian distribution
		The Gaussian (or `normal') distribution is a core ingredient of much of both theoretical and experimental science.
		Then we shall show that it can be be viewed as a special case of the binomial distribution.
		The Gaussian distribution is a special case of the binomial distribution.
	www.ph.ed.ac.uk /~alastair/probstats/contents/fundamentaldists/gaussian/node1.html (314 words)

	Algorithms for Molecular Biology \| Full text \| Pattern statistics on Markov chains and sensitivity to parameter ...
		In this paper, we have chosen to use a binomial approximation as it provides an expression which is analytically differentiable and is known to be a good heuristic to the problem [8].
		As the binomial approximation is supposed to be close to the exact solution, we expect the standard deviation obtained with other statistical methods to remain close to σ.
		As pattern statistics computed through binomial approximations are close to the exact statistics [8], the value of σ should not differ a lot when another statistical method is used.
	www.almob.org /content/1/1/17 (4110 words)

	[No title]
		Unifying Features In generalized linear models, the defining characteristic of the model is the random component of the model which specifies the observations are independent and come from an exponential family distribution.
		With g(mu)=LOG[mu/(1-mu)] for binomial data the mean mu is bounded between 0 and 1, yet the range of g(mu) is also the entire set of real numbers.
		Because the variance of a response may depend on its mean (that is, nonhomogeneous variance), generalized linear models assume that VAR(y) = f[V(mu)] (3) where V() is some known variance function appropriate for the particular type of response data.
	darkwing.uoregon.edu /~robinh/gnmd03_basics.txt (1261 words)

	PlanetMath: Gaussian polynomials
		with 1, then we obtain the familiar integers, factorials, and binomial coefficients.
		This is version 5 of Gaussian polynomials, born on 2001-10-19, modified 2006-02-18.
		(Combinatorics :: Enumerative combinatorics :: Factorials, binomial coefficients, combinatorial functions)
	planetmath.org /encyclopedia/GaussianPolynomials.html (72 words)

	510n1
		is called the binomial distribution The distribution is an example of a discrete distribution.
		is Gaussian, only that it has a finite mean and a variance.
		The probability distribution for the distance traveled after one or a few collisions will not be Gaussian, but the central limit theorem becomes approximately valid after a few collisions.
	www.physics.ubc.ca /~birger/510n1/index.html (661 words)

	Lecture27
		Produces an object of class "glm" which is a generalized linear fit of the data.
		Families supported are gaussian, binomial, poisson, Gamma, inverse.gaussian and quasi.
		Functions like binomial produce a family object, but can be given without the parentheses.
	www.missouri.edu /~tadgw3/stat305/lecture27.html (703 words)

	How to choose a statistical test -- Eric Eisenstein
		Even if the population is Gaussian, it is impossible to analyze such data with a parametric test since you don't know all of the values.
		If the data are not sampled from a Gaussian distribution, consider whether you can transform the values to make the distribution become Gaussian (or at least symmetric).
		When you use a nonparametric test with data from a Gaussian population, the P values tend to be too high.
	www.people.cornell.edu /pages/eme23/whichtest.htm (1744 words)

	Distribution Functions
		The binomial distribution function specifies the number of times (x) that an event occurs in n independent trials where p is the probability of the event occurring in a single trial.
		Use of the Gaussian distribution may be necessary for large values of n.
		With the parameters as defined above, the conditions for validity of the binomial distribution are
	hyperphysics.phy-astr.gsu.edu /hbase/math/disfcn.html (245 words)

	10.20 Mathematics and Statistics
		is descriptive statistics (including histograms, stem-and-leaf plots and box plots), elementary probability, discrete random variables, the binomial distribution, the normal distribution, sampling distribution, estimation and hypothesis testing including both one and two sample tests, paired comparisons, chi-square test, correlation and regression.
		Prerequisite: Mathematics 1000 or 6 credit hours in first year courses in Mathematics or registration in at least semester 3 of a B.N. program or permission of the head of department.
		Material includes descriptive statistics, elementary probability, binomial distribution, normal distribution, sampling distribution, estimation and hypothesis testing (both one and two sample cases), chi-square test, one way analysis of variance, correlation and simple linear regression.
	www.mun.ca /regoff/calendar/sectionNo=SWGC-1028 (1401 words)

	Ed231C: Generalized Linear Models
		Growing out of the work of Nelder and Wedderburn (1972) and McCullagh and Nelder (1989), generalized linear models provides a unified framework which can be applied to various 'linear' models.
		Of course, if all that glm could do was duplicate OLS, logistic, poisson and negative binomial regression that it would not appear to be very useful.
		However, it is possible to combine distribution families and link functions in ways that do not duplicate existing estimation procedures.
	www.gseis.ucla.edu /courses/ed231c/notes1/glm.html (966 words)

	BioMed Central \| Full text \| Canine faecal contamination and parasitic risk in the city of Naples (southern Italy)
		Negative binomial regression models and Gaussian random effects models were used to analyze the association between faeces count and human population density taking into account for extraPoisson variability.
		The results of the negative binomial regression model showed a positive association between the number of canine faeces and the human population density (likelihood ratio chi-square = 11.8; 1 df; P < 0.001).
		It should be noted that the FLOTAC technique and the aforementioned two flotation solutions were selected based on their efficacy in floating the parasitic elements found in dog faeces as determined by us in an unpublished preliminary study (data not shown).
	www.biomedcentral.com /1746-6148/2/29 (3030 words)

	PlanetMath: Gaussian polynomials
		with 1, then we obtain the familiar integers, factorials, and binomial coefficients.
		This is version 5 of Gaussian polynomials, born on 2001-10-19, modified 2006-02-18.
		(Combinatorics :: Enumerative combinatorics :: Factorials, binomial coefficients, combinatorial functions)
	www.planetmath.org /encyclopedia/QBinomialCoefficients.html (72 words)

	The Gaussian distribution
		This is the famous Gaussian distribution function, named after the German mathematician Carl Friedrich Gauss, who discovered it whilst investigating the distribution of errors in measurements.
		The Gaussian distribution is only valid in the limits
		(2.82)-(2.84) are indeed true by substituting in the Gaussian probability density, Eq.
	physics.ship.edu /~mrc/thermo/ut_thermo/node19.html (508 words)

	Application to the binomial distribution
		Let us now apply what we have just learned about the mean, variance, and standard deviation of a general distribution function to the specific case of the binomial distribution function.
		were absent, it would just reduce to the binomial expansion, which we know how to sum.
		The term in square brackets is the familiar binomial expansion, and can be written more succinctly as
	farside.ph.utexas.edu /teaching/sm1/lectures/node19.html (289 words)

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