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Topic: Exponential family

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Uniform distribution (continuous)

Prior distribution

Exponential distribution

Gamma distribution

Laplace distribution

Cauchy distribution

Binomial distribution

Cumulative distribution function

Bernoulli distribution

Bayesian statistics

Statistical hypothesis testing

List of integrals of exponential functions

Exponential decay

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Rayleigh distribution

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	PlanetMath: exponential family
		as a nuisance parameter, belongs to the exponential family.
		Similarly, the Poisson, binomial, Gamma, and inverse Gaussian distributions all belong to the exponential family and they are all in canonical form.
		This is version 4 of exponential family, born on 2004-07-27, modified 2006-09-12.
	www.planetmath.org /encyclopedia/ExponentialFamily.html (241 words)

	NationMaster - Encyclopedia: Parametric model (Site not responding. Last check: 2007-10-29)
		In statistics, a parametric model is a parametrized family of probability distributions, one of which is presumed to describe the way a population is distributed.
		This parametrized family is both an exponential family and a location-scale family In probability and statistics, the exponential family is an important class of probability distributions.
		The family of Poisson distributions is an exponential family.
	www.nationmaster.com /encyclopedia/Parametric-model (620 words)

	Exponential family - Definition, explanation
		The term exponential family is also frequently used to refer to any particular concrete case, i.e., any parametrized family of probability distributions of this form, determined by a choice of H and T.
		The exponential family makes Bayesian estimation procedures very straightforward, because they can be simply expressed in terms of using the observed values of the sufficient statistics to update the parameters of the conjugate prior.
		According to the Pitman-Koopman-Darmois theorem, only in exponential families is there a sufficient statistic whose dimension remains bounded as sample size increases.
	www.calsky.com /lexikon/en/txt/e/ex/exponential_family.php (1353 words)

	exponential - Hutchinson encyclopedia article about exponential (Site not responding. Last check: 2007-10-29)
		In mathematics, descriptive of a function in which the variable quantity is an exponent (a number indicating the power to which another number or expression is raised).
		Exponential functions and series involve the constant e = 2.71828....
		Exponential functions are basic mathematical functions, written as e
	encyclopedia.farlex.com /exponential (254 words)

	Exponential family - Wikipedia, the free encyclopedia
		In probability and statistics, an exponential family is any class of probability distributions having a certain form.
		There are both discrete and continuous exponential families that are useful and important in theoretical or practical work.
		The normal, gamma, chi-square, beta, Dirichlet, Bernoulli, binomial, multinomial, Poisson, negative binomial, geometric, and Weibull distributions are all exponential families.
	en.wikipedia.org /wiki/Exponential_family (1589 words)

	[No title]
		Each curve in a family is determined by the value(s) of parameter(s), that is, numbers that dictate what the curve looks like in a way like the slope and intercept of a line dictate what that line looks like.
		Determining which family of distributions a population's distribution falls into is called modeling, while picking out which member of that family best fits the histogram of a sample from that population is called parameter estimation.
		Find four families of distributions that have at least one member whose shape is similar to the members of the exponential family.
	stat.tamu.edu /ftp/pub/SQ/dist.hlp (1105 words)

	Recent Papers of Robert L. Devaney
		In this paper we describe a family of rational maps of the complex plane that feature infinitely many distinct parameter values for which the corresponding Julia set is a Sierpinski curve (sometimes called a Sierpinski carpet).
		We show that there are many itineraries for the complex exponential map for which the corresponding set of points is an indecomposable continuum, not a hair, as occurs in the case of bounded regular sequences.
		We describe the hyperbolic components of the parameter plane for the complex exponential family using two tools: a parameter plane kneading sequence and a dynamical plane kneading sequence.
	math.bu.edu /people/bob/papers.html (2527 words)

	Exponential family (Site not responding. Last check: 2007-10-29)
		The term exponential family is also frequently used to refer any particular concrete case i.e.
		According to the Pitman-Koopman-Darmois theorem only in families is there a sufficient statistic whose dimension remains bounded as sample increases.
		In the case of a likelihood is an exponential family there exists a prior.
	www.freeglossary.com /Exponential_family (587 words)

	Exponential tree: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-29)
		A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value....
		(the exponential family is an important class of probability distributions....
		The rule of 70 is a financial term derived to determine the time it takes for the value of money to halve due to a given inflation rate....
	www.absoluteastronomy.com /encyclopedia/e/ex/exponential_tree.htm (504 words)

	[No title]
		It might be useful to draw a "family tree" for each one to help you with the math.
		Family C: C has three children and each of them has three children.
		For family B there are twice as many children each generation and for family D there are four times as many.
	www.col-ed.org /cur/math/math51.txt (1178 words)

	I-Africa USA estimator, meer informatie over estimator
		In probability and statistics, the exponential family is an important class of probability distributions.
		There are both discrete and continuous members of the exponential family which are useful and important in theoretical or practical work.
		The term exponential family is also frequently used to refer to any particular concrete case, i.e., any parametrized family of probability distributions of this form, determined by a choice of H and T.
	www.iafrica.org /usa/estimator.htm (1260 words)

	Citations: A generalization of principal component analysis to the exponential family - Collins, Dasgupta, Schapire ...
		6.2 Exponential family PCA To duplicate exponential family PCA [13] we can set the prediction link f arbitrarily and let the parameter links g and h be large multiples of the identity.
		As long as we choose a link function that corresponds to an exponential family distribution log likelihood, and as long as the link and loss....
		Exponential Family PCA for Belief Compression in POMDPs - Roy, Gordon (2003)
	citeseer.ist.psu.edu /context/2030388/629302 (1619 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Such a statistic is known as a sufficient statistic.
		A sufficient statistic for a parameter of a distribution exists if and only if the distribution forms an exponential family.
		Statisticians identify such distributions as belonging to exponential families.
	www.worldhistory.com /wiki/E/Exponential-family.htm (133 words)

	Exponential family (Site not responding. Last check: 2007-10-29)
		The term exponential family is also frequently used to refer to any particular concrete case, i.e., any parametrizedfamily of probability distributions of this form.
		are independent identically distributed random variables whose distribution is known to be insome family of probability distributions.
		In Bayesian statistics a prior distribution is multiplied by a likelihood function and then normalised to produce a posteriordistribution.
	www.therfcc.org /exponential-family-182335.html (499 words)

	Homepage for Michael Sørensen
		We consider ergodic diffusion processes for which the class of invariant measures is an exponential family, and study inference based on the class of invariant probability measures when the diffusion has been observed at discrete time points.
		It is investigated how the usual exponential family inference, which can be done by means of standard statistical computer packages, works when the observations are from a diffusion process.
		For curved exponential families of stochastic processes a natural and often studied sequential procedure is to stop observation when a linear combination of the coordinates of the canonical process crosses a prescribed level.
	www.math.ku.dk /~michael (1605 words)

	Rev. Ted Said 9-23-03 (Site not responding. Last check: 2007-10-29)
		Exponential thinking will help us grow as individuals, as a church family, and will impact our community.
		Exponential thinking is the foundation to the forty days of purpose campaign.
		Exponential growth is caused by God-and can't be programmed or predicted.
	www.secondpres.info /revtedsaid/rts9-23-02.htm (546 words)

	introduction to function families
		This family consists of all functions whose graphs are parabolas with vertical axes of symmetry (i.e., all parabolas which open straight up or down).
		The family is y = ax^2 + bx + c = 1 x^2 + b x + 1, or y = x^2 + bx + 1, with -3 < b < 5.
		Sketch the graph of the exponential family y = 2^x + c for the values c = -3 to 3.
	www.vhcc.edu /pc1spring99/basic_function_families/introduction_to_function_families.htm (1737 words)

	Exponential Family PCA (Site not responding. Last check: 2007-10-29)
		CDS02] demonstrated that PCA can be generalized to a range of loss functions by modeling the data with different exponential families of probability distributions such as Gaussian, binomial, or Poisson.
		Thus, choosing the exponential link function (6) corresponds to minimizing the unnormalized KL divergence between the original belief and its reconstruction.
		The exponential link function corresponds to a Poisson error model for each component of the reconstructed belief.
	www.cs.cmu.edu /afs/cs.cmu.edu/project/jair/pub/volume23/roy05a-html/node4.html (1263 words)

	exponentially (Site not responding. Last check: 2007-10-29)
		Exponentially Large Extra Dimensions Exponentially Large Extra Dimensions We show how the presence of a very light scalar with a cubic self-interaction in six dimensions can stabilize the extra dimensions at radii which are naturally...
		A note about exponentially attracting invariant manifold of ODEs A note about exponentially attracting invariant manifold of ODEs In this paper, we give an affirmative answer to a problem posed by Ryashko and Shnol (2003 Nonlinearity 16 147-60...
		Harmonic oscillator with exponentially decaying mass Harmonic oscillator with exponentially decaying mass The problem of a harmonic oscillator with varying mass parameter is reduced by canonical transformation to the corresponding constant mass...
	www.uk20.co.uk /search.php?q=exponentially (435 words)

	Review of "Exponential Family Nonlinear Models" by Bo-Cheng Wei (Site not responding. Last check: 2007-10-29)
		If we abandon this assumption of link-linearity and instead allow the expected values to be general functions of the regression parameters then we arrive at generalized nonlinear models or, in the terminology of this book, exponential family nonlinear models.
		The usual likelihood computations for exponential family models, such as maximum likelihood estimators, standard errors, the deviance, residuals and influence, are all covered in this book.
		The first two, fairly short, chapters of the book define exponential family nonlinear models and derive the usual first order likelihood calculations.
	www.statsci.org /smyth/pubs/weiefnm.html (892 words)

	Papers of Gareth E. Roberts
		A family of counterexamples is given in the five-body problem (including the Newtonian case) where one of the masses is taken to be negative.
		We also show that certain "hairs" in the parameter plane for the exponential are limits of corresponding external rays for the polynomial families.
		This family persists in similar potential functions, including the logarithmic potential used to describe the motion of point vortices in a plane of fluid.
	mathcs.holycross.edu /~groberts/Papers/papers.html (1124 words)

	Hierarchical mixtures-of-experts for exponential family regression models: approximation and maximum likelihood ...
		We consider hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form $\psi(\alpha + \mathbf{x}^T \mathbf{\beta})$ are mixed.
		Suppose the true response $y$ follows an exponential family regression model with mean function belonging to a class of smooth functions of the form $\psi(h(\mathbf{x}))$ where $h(\cdot)\in W_{2; K_0}^{\infty}$ (a Sobolev class over $[0, 1]^s$).
		We also provide conditions under which the mean-square error of the estimated mean response obtained from the maximum likelihood method converges to zero, as the sample size and the number of experts both increase.
	projecteuclid.org /getRecord?id=euclid.aos/1018031265 (566 words)

	Please see PDF version
		The third section introduces an exponential family of random trees where the number of leaves is the sufficient statistic for the family's natural parameter.
		As a result, we have an exponential family of combinatorial objects which have a central limit theory and which are amenable to practical simulation.
		Since this construction brings tools of statistical mechanics, the exponential family, and the Monte Carlo method into focus on problems as a priori remote as the coefficient of the Hermite polynomial and the number of leaves of a random tree, the Gibbs method would seem to merit much further study in combinatorics.
	www-stat.wharton.upenn.edu /~steele/Publications/HTML/GMoCOa.html (4326 words)

	Definition of exponential growth
		1:...tive]] [[algebra]]s, which is equivalent to the [[exponential function]] of the [[integral]] in the [[commutati...
		3: In [[differential geometry]], the '''exponential map''' is the map from (a subset of) the tangent...
		impeded in the case of likelihoods which are not exponential families because of the lack of [[sufficient stat...
	www.wordiq.com /search/exponential+growth.html (798 words)

	Rohana Karunamuni
		Empirical Bayes two-action problem for the continuous one-parameter exponential family with errors in variables.
		Empirical Bayes estimation for the continuous one-parameter exponential family with errors in variables.
		Empirical Bayes sequential estimation for exponential families: The untruncated component.
	www.math.ualberta.ca /Karunamuni_R.html (606 words)

	Nicholas Roy -- Research
		The dimensionality of the belief space is reduced by exponential family Principal Components Analysis (Collins et al.
		``Exponential Family PCA for Belief Compression in POMDPs''.
		The acoustic signature arising from the contact is then used to classify the floor type by comparing a windowed power spectrum of the acoustic signature with one of a family of prototypical signatures generated statistically from the same material.
	web.mit.edu /nickroy/www/research.html (1053 words)

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