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	Hyperbolic secant distribution - Wikipedia, the free encyclopedia
		In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function.
		The hyperbolic secant distribution shares many properties with the standard normal distribution: it is symmetric with unit variance and zero mean, median and mode, and its pdf is proportional to its characteristic function.
		However, the hyperbolic secant distribution is leptokurtic, that is, it has a more acute peak near its mean, compared with the standard normal distribution.
	en.wikipedia.org /wiki/Hyperbolic_secant_distribution (372 words)

	Normal distribution Summary
		The fundamental importance of the normal distribution as model of quantitative phenomena in the natural and behavioral sciences, is due to the central limit theorem (the proof of which requires rather advanced undergraduate mathematics).
		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 Abraham de Moivre in an article in 1734 (reprinted in the second edition of his The Doctrine of Chances, 1738) in the context of approximating certain binomial distributions for large n.
	www.bookrags.com /Normal_distribution (4551 words)

	Normal distribution (Site not responding. Last check: 2007-11-07)
		The standard normal distribution is the normal distribution with a mean of zero and a variance of one (the green curves in the plots to the right).
		For example, the sampling distribution of the sample mean is approximately normal, even if the distribution of the population the sample is taken from is not normal.
		The cumulative distribution function (cdf) of a probability distribution, evaluated at a number (lower-case) x, is the probability of the event that a random variable (capital) X with that distribution is less than or equal to x.
	libraryoflibrary.com /E_n_c_p_d_Normal_distribution.html (5796 words)

	Probability distribution (Site not responding. Last check: 2007-11-07)
		A distribution is called discrete if its cumulative distribution function consists of a sequence of finite jumps, which means that it belongs to a discrete random variable X: a variable which can only attain values from a certain finite or countable set.
		The Probability distribution of the sum of two random variables is the convolution of each of their distributions.
		The triangular distribution on [''a'', b], a special case of which is the distribution of the sum of two uniformly distributed random variables (the convolution of two uniform distributions).
	probability-distribution.mindbit.com (1304 words)

	Poisson distribution Summary
		For a binomial distribution one must know both the number of successful events as well as the number of unsuccessful events, whereas in the Poisson distribution one needs to know only the mean number of successful occurrences of an event.
		For temporally distributed events, the Poisson distribution is the probability distribution of the number of events that would occur within a preset time, the Erlang distribution is the probability distribution of the amount of time until the nth event.
		Skellam distribution, the distribution of the difference of two Poisson variates, not necessarily from the same parent distribution.
	www.bookrags.com /Poisson_distribution (2272 words)

	RANDOM NUMBER GENERATION (LUC DEVROYE)
		For many distributions, it is possible to generate a random variate in one assignment statement using only simple mathematical functions and ordinary arithmetic operations.
		We give random variate generators for the generalized hyperbolic secant distribution and related families such as Morris's skewed generalized hyperbolic secant family and a family introduced by Laha and Lukacs.
		We derive useful distributional representations for the discrete stable distribution of Steutel and Van Harn, the discrete Linnik distribution introduced by Pakes, and a discrete distribution of Sibuya.
	cg.scs.carleton.ca /~luc/rng.html (1485 words)

	Negative binomial distribution - Wikipedia, the free encyclopedia
		Third, the negative binomial distribution arises as a continuous mixture of Poisson distributions where the mixing distribution of the Poisson rate is a gamma distribution.
		In this sense, the negative binomial distribution is the "inverse" of the binomial distribution.
		Thus the negative binomial distribution bears the same relationship to the negative-integer-exponent case of the binomial theorem that the binomial distribution bears to the positive-integer-exponent case.
	en.wikipedia.org /wiki/Negative_binomial_distribution (1643 words)

	Probability distribution - Wikipedia, the free encyclopedia
		The probability distribution of the sum of two independent random variables is the convolution of each of their distributions.
		The rectangular distribution is a uniform distribution on [-1/2,1/2].
		The F-distribution, which is the distribution of the ratio of two (normalized) chi-square distributed random variables, used in the analysis of variance.
	en.wikipedia.org /wiki/Probability_distribution (1551 words)

	Student's t-distribution - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-11-07)
		-distribution or Student's t-distribution is a probability distribution that arises in the problem of estimating the mean of a normally distributed population when the sample size is small.
		Student's distribution arises when (as in nearly all practical statistical work) the population standard deviation is unknown and has to be estimated from the data.
		The overall shape of the probability density function of the t-distribution resembles the bell shape of a normally distributed variable with mean 0 and variance 1, except that it is a bit lower and wider.
	search.com.com.cob-web.org:8888 /reference/T_statistic (1509 words)

	RePEc
		However, a drawback of this distribution is represented by the technical dificulties due to the evaluation of moments, especially in the case of fractional degrees of freedom.
		The main advantage of the GSH distribution over the Student-t distribution is that all the moments are finite for each value of the shape parameter.
		The distribution is symmetric with respect to the mean, but we show that it is still possible to obtain the density in a closed form introducing a skewness parameter according to the method proposed by Fernandez and Steel.
	www.inomics.com /cgi/repec?handle=RePEc:bep:sndecm:8:2004:2:1212-1212 (218 words)

	Beta distribution - Wikipedia, the free encyclopedia
		B(i,j) with integer values of i and j is the distribution of the i-th highest of a sample of i+j-1 independent random variables uniformly distributed between 0 and 1.
		Beta distributions are used extensively in Bayesian statistics, since beta distributions provide a family of conjugate prior distributions for binomial (including Bernoulli) and geometric distributions.
		For this reason, the Beta distribution - along with the triangular distribution - is used extensively in PERT, CPM and other project management / control systems to describe the time to completion of a task.
	en.wikipedia.org /wiki/Beta_distribution (600 words)

	Chapter 7. Analyses of the Axial Load Tests at the Route 351 Bridge, A Laboratory and Field Study of Composite Piles ...
		Hyperbolic stress-strain models have been found to adequately represent the nonlinear behavior of most soils (Kondner 1963, Kondner and Zelasko 1963, Duncan and Chang 1970).
		The stiffness measured using conventional laboratory tests is lower because it is affected by factors such as the quality of the soil sample, small disturbances during sample setup in the test apparatus, seating of loading platen, and small misalignments of loading ram (Atkinson 2000).
		The conventional hyperbolic model may be more appropriate to capture the soil nonlinearity when the initial modulus used is from conventional laboratory tests.
	www.tfhrc.gov /structur/pubs/04043/07.htm (8940 words)

	Logistic distribution - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-11-07)
		The logistic distribution is closely related to the logistic function and the logistic equation which also follow from the work of Verhulst.
		This distribution has longer tails than the normal distribution and a higher kurtosis of 1.2 (compared with 0 for the normal distribution).
		Because the pdf can be expressed in terms of the square of the hyperbolic secant function "sech", it is sometimes referred to as the sech-square(d) distribution.
	en.wikipedia.org.cob-web.org:8888 /wiki/Logistic_distribution (446 words)

	Amazon.com: "hyperbolic secant distribution": Key Phrase page (Site not responding. Last check: 2007-11-07)
		See all pages with references to hyperbolic secant distribution.
		including the generalized hyperbolic secant distribution, and Table 3.2 summarizes the unit deviances for all six distributions in the Morris class.
		Let X have pdf f(x) = Sech[.x]/ir, x e R, which is known as the Hyperbolic Secant distribution.
	www.amazon.com /phrase/hyperbolic-secant-distribution (328 words)

	Stat 5601 (Geyer) Hyperbolic Secant Distribution (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-11-07)
		The hyperbolic secant distribution is the probability distribution with density proportional to the hyperbolic secant function, which is the reciprocal of the hyperbolic cosine function, the hyperbolic cosine being defined by
		This distribution is not used much in applications, but it does have two curious features.
		The hyperbolic secant density is shown in the Rweb plot below.
	www.stat.umn.edu.cob-web.org:8888 /geyer/old02/5601/examp/hsec.html (123 words)

	MIT Lincoln Laboratory - Parallel Programming with MatlabMPI
		Returns the ranges of global indices for all processors in the map of distributed array D on all processors in communication scope.
		Given collected distributed data in grid layout, reconstructs the original object according to data distribution.
		Returns the processor grid onto which the distributed array is mapped.
	www.ll.mit.edu /pMatlab (1449 words)

	Sound baffling device - Patent 6091825
		The sound baffling device of claim 1 or claim 2 characterized by the splitting of the sound energy into a reflected and a transmitted component, so that the distribution of said reflected and transmitted component is determined by the shape of the enclosure in combination with the degree of rarefaction therein, and;
		The sound baffling device of claim 10 characterized by the splitting of the sound energy into a reflected and a transmitted component, such that the distribution of said reflected and transmitted component is determined by the shape of the enclosure in combination with the degree of rarefaction therein, and;
		The spirals may also be hyperbolic, parabolic, or the spiral of Archimedes, with equations r@=a, (r-a).sup.2 =4ak@, r=a@, respectively.
	www.freepatentsonline.com /6091825.html (16975 words)

	secant - OneLook Dictionary Search
		Secant, Secant : A Glossary of Mathematical Terms [home, info]
		secant, secant, secant : PlanetMath Encyclopedia [home, info]
		Phrases that include secant: arc secant, hyperbolic secant, hyperbolic secant distribution, secant angles, secant modulus of elasticity, more...
	www.onelook.com /?w=secant (248 words)

	Golden State Software Systems, Inc.; The IBM iSeries AS/400* Software Development Specialists
		Hyperbolic Arc Cosecant of an angle - Returns an angle in any of eight different angle measurement units for a given hyperbolic cosecant.
		Hyperbolic Arc Secant of an angle - Returns an angle in any of eight different angle measurement units for a given hyperbolic secant.
		Hyperbolic Arc Tangent of an angle - Returns an angle in any of eight different angle measurement units for a given hyperbolic tangent.
	www.gsssi.com /fjlist.html (3911 words)

	Command Line Help
		FINV Inverse of the F cumulative distribution function.
		NBININV Inverse of the negative binomial cumulative distribution function (cdf).
		NCFINV Inverse of the noncentral F cumulative distribution function (cdf).
	www.rit.edu /~pnveme/EMEM682n/wk1/commandhelp.html (283 words)

	[No title]
		RANDN(N) is an N-by-N matrix with random entries, chosen from a normal distribution with mean zero, variance one and standard deviation one.
		Each column of n contains the results for the corresponding column of Y. n = hist(Y,x), where x is a vector, returns the distribution of Y among length(x) bins with centers specified by x.
		Image histogram An image histogram is a chart that shows the distribution of intensities in an indexed or intensity image.
	www.ee.unlv.edu /~regent/SPACE/MATHLAB_1.doc (4188 words)

	AST_MATHMAP - Create a MathMap
		ACOSH(X): Inverse hyperbolic cosine of X. ACOTH(X): Inverse hyperbolic cotangent of X. ACSCH(X): Inverse hyperbolic cosecant of X. AINT(X): Integer part of X (round towards zero), same as INT(X).
		COSH(X): Hyperbolic cosine of X. COTH(X): Hyperbolic cotangent of X. CSCH(X): Hyperbolic cosecant of X. DIM(X1, X2): Returns X1-X2 if X1 is greater than X2, otherwise 0.
		SECH(X): Hyperbolic secant of X. SIGN(X1, X2): Absolute value of X1 with the sign of X2 (transfer of sign).
	star-www.rl.ac.uk /~dsb/ast/sun210.htx/node294.html (2524 words)

	Harvard University Statistics Department David Esch Colloquium (Site not responding. Last check: 2007-11-07)
		The distribution will be introduced, along with its basic properties, in particular heavy tails and skewness, which have many potential uses in Statistical Modeling.
		This model extends work by Nowak and Kolaczyk, 2000, in which a wavelet-like multiscale basis is used as a prior distribution to regularize the image reconstruction.
		Morris' NEF6 distribution is the Natural Exponential Family (NEF) generated by the Generalized Hyperbolic Secant distribution, which represents convolutions and divisions of the variable whose density is proportional to the hyperbolic secant function.
	www.stat.harvard.edu /Research/Colloquia_Series/2002-2003/David_Esch.html (333 words)

	Estimation Theory: Problems (Site not responding. Last check: 2007-11-07)
		Although the maximum likelihood estimation procedure was not clearly defined until early in the 20th century, Gauss showed in 1905 that the Gaussian density 1 was the sole density for which the maximum likelihood estimate of the mean equaled the sample average.
		Let the observations r(l) consist of statistically independent, identically distributed Gaussian random variables having zero mean but unknown variance.
		Despite this fact, the Gaussian and other similarly unfriendly random variables can be generated using tabulated rather than analytic forms for the distribution function.
	cnx.org /content/m11221/latest (1664 words)

	Communications in Statistics - Theroy and Methods Vol. 34
		Distribution of a Sum of Weighted Central Chi-square Variables...
		Series Representation of Non-null distribution of the Square of Sample Multiple Correlation Coefficient by use of the Mellin Integral Transform...
		The Distribution of a Ratio of Quadratic Forms in Noncentral Normal Variables...
	www.math.mcmaster.ca /bala/comstat/cis_tm_v34.html (1780 words)

	GNU libmatheval manual
		This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
		VERBATIM COPYING You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License.
		You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.
	www.gnu.org /software/libmatheval/manual/libmatheval.html (6988 words)

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