The phrase T distribution may refer to Student s t test in univariate statistics, Student s t distribution in univariate probability theory, Hotelling s T square distribution in multivariate statistics. Multivariate Student distribution . disambig Category Probability distributions ... more details
wiktionarypar distribution tocright Distribution may refer to In mathematics, science, and technology In mathematics Distribution mathematics , generalized functions used to formulate solutions of partial differential equations Probability distribution , the probability of a particular values or value range of a variable Cumulative distribution function , in which the probability of a value is a function of that value Frequency distribution , a list of the values recorded in a sample Inner distribution and outer distribution , in coding theory Distribution differential geometry , a subset of the tangent ... state space Distribution of terms , a situation in which all members of a category are accounted ... elementary algebra In science Complementary distribution , in linguistics, a relationship between elements found in opposite environments Distribution pharmacology , the transfer of a drug within the body Distribution function , in physics, the number of particles per unit volume in phase space Population distribution , the geographical area in which a species lives Spectral power distribution , in color science, the power per unit area per unit wavelength of an illumination Trip distribution , part ... distribution , the final stage in the delivery of electricity Electronic brakeforce distribution , an automotive ... , the coordinated use of physically distributed computers for tasks or storage Software distribution, a bundle of a specific software already compiled and configured Linux distribution , one of several distributions built on the Linux kernel Distribution concurrency , the projection operator in a history monoid, a representation of the histories of concurrent computer processes Key distribution center , part of a cryptosystem intended to reduce the risks inherent in exchanging keys Content distribution , publishing and web design as method to provide information Digital distribution , publishing media digitally Distribution of elements in the distributed element model of electric circuits ... more details
Fisher distribution may refer to Fisher s noncentral hypergeometric distribution Fisher s z distribution Fisher s fiducial distribution Fisher Bingham distribution F distribution , also called Fisher Snedecor distribution or Fisher F Distribution Fisher Tippett distribution Von Mises Fisher distribution disambig ... more details
Unreferenced stub auto yes date December 2009 A distribution deal is a legal agreement between one party and another, to handle distribution business distribution of a product. DEFAULTSORT Distribution Deal Category Commercial item transport and distribution Business stub ... more details
Uniform distribution may refer to Probability theory Uniform distribution discrete Discrete uniform distribution Uniform distribution continuous Continuous uniform distribution Other Uniform distribution modulo 1 , see Equidistributed sequence Uniform distribution ecology , a type of species distributionDistribution of military uniform s disambig de Gleichverteilung eo Uniforma distribuo eu Banaketa uniforme argipena fr Loi uniforme nl Uniforme verdeling pl Rozk ad jednostajny ru vi Ph n b ng u nhi n u ... more details
The lambda distribution is either of two probability distribution s used in statistics Tukey lambda distribution Tukey s lambda distribution is a shape conformable distribution used to identify an appropriate common distribution family to fit a collection of data to. Wilks lambda distribution is an extension of George W. Snedecor Snedecor s F distribution for matrix mathematics matricies used in multivariate hypothesis testing, especially with regard to the likelihood ratio test and multivariate analysis of variance . disambig Category Probability distributions ... more details
Unreferenced date January 2007 In statistical hypothesis testing , the null distribution is the probability distribution of the test statistic when the null hypothesis is true. In an F test , the null distribution is an F distribution . DEFAULTSORT Null Distribution Category Statistical inference Category Probability distributions Category Statistical terminology Statistics stub ko ... more details
Unreferenced date February 2007 In statistics , a univariate distribution is a probability distribution of only one random variable . This is in contrast to a multivariate distribution , the probability distribution of a random vector . See also Univariate Bivariate distribution Further reading cite doi 10.1198 000313008X270448 Common univariate probability distributions DEFAULTSORT Univariate Distribution Category Types of probability distributions Category Statistical terminology Stat stub ... more details
A system distribution is a collection of software designed to be installed into a computer, it is sometimes erroneously called an operating system . Examples of a system distribution are Microsoft Windows , Mac OS X and Ubuntu operating system Ubuntu . It can also refer to Linux distribution Berkeley Software Distribution disambig ... more details
Distribution mathematics Tempered distributions and Fourier transform Distribution mathematics tempered distributions on Euclidean space Tempered representation tempered distributions on semisimple groups disambig ... more details
In mathematics and statistics , an asymptotic distribution is a hypothetical distribution that is in a sense the limiting distribution of a sequence of distributions. One of the main uses of the idea of an asymptotic distribution is in providing approximations to the cumulative distribution function s of statistical estimator s. Definition A sequence of distributions corresponds to a sequence of random variables Z sub i sub for i 1, 2, ... In the simplest case, an asymptotic distribution exists if the probability distribution of Z sub i sub converges to a probability distribution the asymptotic distribution as i increases see Convergence of random variables Convergence in distribution convergence in distribution . A special case of an asymptotic distribution is when the sequence of random variables always approaches zero that is, the Z sub i sub go to 0 as i goes to infinity. Here the asymptotic distribution is a degenerate distribution , corresponding to the value zero. However, the most usual sense in which the term asymptotic distribution is used arises where the random variables Z ... converges in distribution to a non degenerate distribution for two sequences a sub i sub and b sub i sub then Z sub i sub is said to have that distribution as its asymptotic distribution. If the distribution function of the asymptotic distribution is F then, for large n , the following approximations ... If an asymptotic distribution exists, it is not necessarily true that any one outcome of the sequence ... distribution to arise as an asymptotic distribution is the normal distribution . In particular, the central limit theorem provides an example where the asymptotic distribution is the normal distribution ... normality. The Binomial distribution seems to be the first asymptotic approximation by a normal distribution compared to the more general case of central limit theorem , convergence of the Binomial to the normal is especially rapid. cn date March 2011 Asymptotic normality of the Binomial distribution ... more details
In statistics , the concept of the shape of the distribution refers to the shape of a probability distribution and it most often arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population. The shape of a distribution may be considered either descriptively, using terms such as J shaped , or numerically, using quantitative measures such as skewness and kurtosis . Considerations of the shape of a distribution arise in statistical data analysis , where simple quantitative descriptive statistics and plotting techniques such as histograms can lead on to the selection of a particular family of distributions for modelling purposes. File Standard deviation diagram.svg right thumb 350px The Normal distribution , often called the bell curve Image Exponential distribution pdf.png thumb Exponential distribution Descriptions of shape The shape of a distribution will fall somewhere in a continuum where a flat distribution might be considered central and where types of departure from this include mounded or unimodal , U shaped, J shaped, reverse J shaped and multi modal. ref Yule & Kendall 1950 Chapter 4 &mdash Frequency Distributions ref A bimodal distribution would have two high points rather than one. The shape of a distribution is sometimes characterised by the behaviours of the tails as in a long or short tail . For example a flat distribution can be said either to have no tails, or to have short tails. A normal distribution is usually regarded as having short tails, while an exponential distribution has exponential tails and a Pareto distribution has long tails. Even in the relatively simple case of a mounded distribution, the distribution may be skewed to the left or skewed to the right, with symmetric corresponding to no skew. See also Shape parameter List of probability distributions Notes Reflist References Yule, G.U., Kendall, M.G. 1950 An Introduction to the Theory of Statistics ... more details
Unreferenced date January 2007 A utilization distribution is a probability distribution constructed from data providing the location of an individual in space at different points in time. See also Home range Local convex hull DEFAULTSORT Utilization Distribution Category Types of probability distributions Statistics stub ... more details
Distribution Select formerly Distribution Musicor, Distribution GAM and Distribution Trans Canada is a Canadian record and video distributor based in Montreal , Quebec in 1965 in music 1965 as Disques Select. It is a wholly owned division of Quebecor Media . History 1965 Company formed as Disques Select. 1971 Company moves to Sainte Catherine Street. 1974 Distribution Musicor opens in Pointe Claire , Quebec . Unrelated to an American record label, Musicor Records . 1977 Disques Select changes into Distribution Select. 1980 Company acquires Services de Musique Trans Canada. 1985 Distribution Select adopts a new logo. 1989 Distribution Musicor and Distribution Trans Canada set up in Pointe Claire. 1993 Distribution Trans Canada ceases operations. 1996 Distribution Musicor joins with Distribution GAM. 2001 Distribution Select ceases the activities of Distribution Musicor and Distribution GAM. Labels Disques Passeport Global Video Perrin Video Disques Musicor Guy Cloutier Communications See also List of record labels External links http www.distributionselect.ca en index.asp Official site cite web url http www.cria.ca gold 1203 g.php title Canadian French and English artists rack up certifications date December 2003 accessdate 2008 12 30 publisher Canadian Recording Industry Association DEFAULTSORT Select Category Quebecor Category Quebec record labels Category Record labels established in 1965 Category Companies based in Montreal Category Article Feedback 5 Canada record label stub Quebec stub fr Distribution Select ... more details
Stationary distribution may refer to The limiting distribution in a Markov chain Steady state analysis and limiting distributions Markov chain The marginal distribution of a stationary process or stationary time series The set of joint probability distribution s of a stationary process or stationary time series In some fields of application, the term stable distribution is used for the equivalent of a stationary marginal distribution, although in probability and statistics the term has a rather different meaning see stable distribution . Crudely stated, all of the above are specific cases of a common general concept. A stationary distribution is a specific entity which is unchanged by the effect of some matrix or operator it need not be unique. Thus stationary distributions are related to eigenvector s for which the eigenvalue is unity. See also Stationary ergodic process Perron&ndash Frobenius theorem Stationary state or ground state in quantum mechanics Category Statistical terminology Category Stochastic processes Category Time series analysis stats stub ... more details
The Wigner distribution is either of two things Wigner semicircle distribution A probability function used in mathematics Eugene Wigner Wigner quasi probability distribution A distribution in phase space encoding, in a convenient representation, properties of quantum mechanical wave functions. Strictly speaking, it is the Wigner map of the density matrix in the Weyl quantization Weyl correspondence . In signal analysis, it is known as the Wigner Ville distribution. It is useful in quantum statistical mechanics, quantum chemistry, optics, quantum computing etc. Eugene Wigner , Hermann Weyl , J. Ville See also Breit Wigner distribution disambiguation disambig nl Wignerdistributie ... more details
Unreferenced date June 2007 Neptune Distribution was a comic distribution company established in Leicester in 1986. It was set up to challenge Titan Books Titan Distribution s monopoly on the United Kingdom UK comic distribution business. The proved to be successful with the company expanding into publishing in 1988 with Trident Comics and later help found Apocalypse Ltd , publishing Toxic , a weekly title meant to compete with 2000 AD comic 2000 AD . However the company expanded too quickly and financial problems meant the distribution side of the company was sold to Diamond Comic Distributors in 1992. Category Neptune Distribution UK comics stub ... more details
In probability , a singular distribution is a probability distribution concentrated on a Null set set of Lebesgue measure zero , where the probability of each point in that set is zero. These distributions are sometimes called singular continuous distributions . Such distributions are not absolutely continuous with respect to Lebesgue measure . A singular distribution is not a discrete probability distribution because each discrete point has a zero probability. On the other hand, neither does it have a probability density function , since the Lebesgue integral of any such function would be zero. An example is the Cantor distribution . See also Singular measure Lebesgue s decomposition theorem External links http eom.springer.de S s085530.htm Springer Encyclopaedia of Mathematics ProbDistributions DEFAULTSORT Singular Distribution Category Probability distributions Category Types of probability distributions Statistics stub probability stub it Distribuzione singolare ... more details
In statistics , a sampling distribution or finite sample distribution is the probability distribution ..., they allow analytical considerations to be based on the sampling distribution of a statistic, rather than on the joint probability distribution of all the individual sample values. Introduction The sampling distribution of a statistic is the probability distributiondistribution of that statistic ... as the distribution of the statistic for all possible samples from the same population of a given size. The sampling distribution depends on the underlying probability distributiondistribution of the population ... used. There is often considerable interest in whether the sampling distribution can be approximated by an asymptotic distribution , which corresponds to the limiting case as n &rarr . For example, consider a normal distribution normal population with mean and variance . Assume we repeatedly ... average value, and the distribution of these averages is called the sampling distribution of the sample mean . This distribution is normal math scriptstyle mathcal N mu, , sigma 2 n math since the underlying ... when the population distribution is not see central limit theorem . An alternative to the sample mean is the sample median . When calculated from the same population, it has a different sampling distribution ... . The mean of a sample from a population having a normal distribution is an example of a simple statistic ... s, Bootstrapping statistics bootstrap methods, or asymptotic distribution theory. Standard error The standard deviation of the sampling distribution of the statistic is referred to as the standard ... math sigma math is the standard deviation of the population distribution of that quantity and n is the size .... Examples class wikitable Population Statistic Sampling distribution Normal distribution Normal math ... N Big mu, , frac sigma 2 n Big math Bernoulli distribution Bernoulli math operatorname Bernoulli p math Sample proportion of successful trials math bar X math Binomial distribution math n bar X sim ... more details
A product distribution is a probability distribution constructed as the distribution of the Product business ... random variables X and Y , the distribution of the random variable Z that is formed as the product math Z XY math is a product distribution . Algebra of random variables main Algebra of random variables The product is one type of algebra for random variables Related to the product distribution are the ratio distribution , sum distribution and difference distribution . More generally, one ... John Wiley & Sons Wiley year 1979 isbn 0 471 01406 0 ref Derivation A way of deriving the product distribution of Z from the joint distribution of the two other random variables, X and Y , is by integration ... right , dx. math This is not always straightforward. Special cases The distribution of the product of two random variables which have lognormal distribution s is again lognormal. This is itself a special ... of the components of the product, the result might be transformed to provide the distribution of the product ... are in some standard families of distributions. The distribution of the product of a random variable having a Uniform distribution continuous uniform distribution on 0,1 with a random variable having a gamma distribution with shape parameter equal to 2, is an exponential distribution . ref name JKB ... 0 471 58494 0 ref A more general case of this concerns the distribution of the product of a random variable having a beta distribution with a random variable having a gamma distribution for some cases ... is again a gamma distribution but with a changed shape parameter. ref name JKB The K distribution is an example of a non standard distribution that can be defined as a product distribution where both components have a gamma distribution . See also Algebra of random variables Notes Reflist References cite journal doi 10.1137 0118065 title The distribution of products of beta, gamma and Gaussian random ... 18 issue 4 pages 721&ndash 737 year 1970 jstor 2099424 cite journal title The distribution of products ... more details
primary sources date July 2008 Image Distribution frame 0a messy.jpg thumb right 150px Unshielded twisted pair copper and optical fiber distribution frame. Image Optical fiber distribution frame 0a.jpg thumb right 150px An optical fiber distribution frame. In telecommunications , a distribution frame is a passive device which terminates cables, allowing arbitrary interconnections to be made. For example, the Main Distribution Frame MDF located at a telephone exchange telephone central office terminates the cables leading to subscribers on the one hand, and cables leading to active equipment such as DSLAM s and telephone switch es on the other. Service is provided to a subscriber by manually wiring a twisted pair called a jumper wire between the telephone line and the relevant DSL or Plain old telephone service POTS line circuit. In broadcast engineering , a distribution frame is a location ... . Types Distribution frames for specific types of signals often have specific acronyms ADF Sound audio distribution frame DDF digital distribution frame VDF video distribution frame ODF or OFDF optical fiber distribution frame ref http patft1.uspto.gov netacgi nph Parser?patentnumber 7142765 US patent 7,142,765 High Density Optical Fiber Distribution Frame ref Modernization Distribution frames may grow to extremely large sizes. In major installations, audio distribution frames can ..., but some urban Telephone exchange exchanges have about 250,000 wires on their Main distribution frame ... to devise so called active distribution frames or Automated Main Distribution Frame s. The principal ... digital mixing console s can act as control point s for a distribution frame or router computing ... through wall s and sometimes floor s and ceiling s to a single point. See also Main distribution frame Intermediate distribution frame Wiring closet Patch panel Splicebox References reflist Category ... Distribution Frame fa fr Tableau lectrique ru ... more details
A dyadic distribution is a specific type of discrete or categorical probability distribution that is of some theoretical importance in data compression . Definition A dyadic distribution on the nonnegative integers 0, 1, 2, ... is a probability distribution whose probability mass function is math f u 2 n u , quad u in U math where n sub u sub is some positive integer . More generally it is a categorical distribution in which the probability assigned to any label is of the above form It is possible to find a code defined on this distribution, which has an average code length that is equal to the entropy . Citation needed date August 2010 No footnotes date July 2010 References Cover, T.M., Joy A. Thomas, J.A. 2006 Elements of information theory , Wiley. ISBN 0471241954 DEFAULTSORT Dyadic Distribution Category Types of probability distributions Category Data compression ... more details
Other uses Weight distribution Mass distribution is a term used in physics and mechanics and describes the spatial distribution of mass within a solid body. In principle, it is relevant also for gas es or liquid s, but on earth their mass distribution is almost homogeneous. Astronomy In astronomy mass distribution has decisive influence on the development e.g. of nebula e, star s and planet s. The mass distribution of a solid defines its center of gravity and influences its dynamical behaviour e.g. the oscillation s and eventual rotation . Mathematical modelling A mass distribution can be modeled as a Measure mathematics measure . This allows point masses, line masses, surface masses, as well as masses given by a volume density function. Alternatively the latter can be generalized to a distribution mathematics distribution . For example, a point mass is represented by a Dirac delta Generalizations delta function defined in 3 dimensional space . A surface mass on a surface given by the equation f x,y,z 0 may be represented by a density distribution g x,y,z f x,y,z , where math g mid nabla f mid math is the mass per unit area. The mathematical model ling can be done by potential theory , by numerical methods e.g. a great number of point mass mass point s , or by theoretical mechanical equilibrium equilibrium figures. Geology In geology the aspects of rock density are involved. Rotating solids Rotation Rotating solids are affected considerably by the mass distribution, either if they are homogeneous or inhomogeneous see Torque , moment of inertia , wobble , wikt imbalance imbalance and stability . Disambiguation needed date August 2011 Related topics gravity , mass function , Bouguer plate , critical mass angular momentum , asymmetry , geoid , isostasy , polar motion mass spectrum , molar mass distribution , atmosphere External links http www.geod.uni bonn.de apmg projekte dfg schwerpunkt texte mass transport proposal spp.pdf Mass distribution of the Earth Category Mechanics ... more details
A soliton distribution is a type of discrete probability distribution that arises in the theory of erasure correcting code s. A paper by Luby ref name Luby Luby, M. 2002 , http ieeexplore.ieee.org xpl freeabs all.jsp?arnumber 1181950 LT Codes , The 43rd Annual IEEE Symposium on Foundations of Computer Science ref introduced two forms of such distributions, the ideal soliton distribution and the robust soliton distribution . Ideal distribution The ideal soliton distribution is a probability distribution on the integers from 1 to N , where N is the single parameter of the distribution. The probability mass function is given by ref name T Tuomas Tirronen 2005 http citeseerx.ist.psu.edu viewdoc download?doi 10.1.1.140.8104&rep rep1&type pdf Optimal Degree Distributions for LT Codes in Small Cases , Helsinki University of Technology. ref math p 1 frac 1 N , math math p k frac 1 k k 1 qquad k 2,3, dots,N . , math Robust distribution The robust form of distribution is defined by adding an extra set of values to the elements of mass function of the ideal soliton distribution and then standardising so that the values add up to 1. The extra set of values, t , are defined in terms of an additional real values parameter &delta which is interpreted as a failure probability and an integer parameter M M < N . Define R as R N M . Then the values added to p i , before the final standardisation, are ref name T math t i frac 1 iM , qquad qquad i 1,2, dots,M 1 , , math math t i frac ln R delta M , qquad i M , , math math t i 0, qquad qquad i M 1, dots,N . , math While the ideal soliton distribution has a mode statistics mode or spike at 1, the effect of the extra component in the robust distribution is to add an additional spike at the value M . See also Luby transform code References reflist Category Discrete distributions Category Coding theory ... more details
In telecommunications , a fading distribution is the probability distribution of the value of Signalling telecommunication signal fading relative to a specified reference level. In the case of phase interference fading , the time distribution of the instantaneous field strength usually approximates a Rayleigh distribution when several signal components of equal amplitude are present. The field strength is usually measured in volts per meter. The fading distribution may also be measured in terms of Power physics power level, where the unit of measure is usually watts per square meter and the expression is in decibel s. References FS1037C MS188 Category Radio frequency propagation fading telecomm stub ... more details
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