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Non-central F-distribution
In probability theory and statistics, the noncentral ''F''-distribution is a continuous probability distribution that is a noncentral generalization of the (ordinary) ''F''-distribution. It describes the distribution of the quotient (''X''/''n''1)/(''Y''/''n''2), where the numerator ''X'' has a noncentral chi-squared distribution with ''n''1 degrees of freedom and the denominator ''Y'' has a central chi-squared distribution with ''n''2 degrees of freedom. It is also required that ''X'' and ''Y'' are statistically independent of each other. It is the distribution of the test statistic in analysis of variance problems when the null hypothesis is false. The noncentral ''F''-distribution is used to find the power function of such a test. Occurrence and specification If X is a noncentral chi-squared random variable with noncentrality parameter \lambda and \nu_1 degrees of freedom, and Y is a chi-squared random variable with \nu_2 degrees of freedom that is statistically indepe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Density Function
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be equal to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. More precisely, the PDF is used to specify the probability of the random variable falling ''within ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled ''CRC Concise Encyclopedia of Mathematics''. The free online version became only partially accessible to the public. In 1999 Weisstein we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Humboldt University Of Berlin
The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humboldt, Johann Gottlieb Fichte and Friedrich Daniel Ernst Schleiermacher as the University of Berlin () in 1809, and opened in 1810. From 1828 until its closure in 1945, it was named the (Royal) Friedrich Wilhelm University of Berlin (FWU Berlin; ). During the Cold War, the university found itself in East Berlin and was ''de facto'' split in two when the Free University of Berlin opened in West Berlin. The university received its current name in honour of Alexander and Wilhelm von Humboldt in 1949. The university is divided into nine faculties including its medical school shared with the Freie Universität Berlin. The university has a student enrollment of around 35,000 students, and offers degree programs in some 171 disciplines from un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boost C++ Libraries
Boost, boosted or boosting may refer to: Science, technology and mathematics * Boost, positive manifold pressure in turbocharged engines * Boost (C++ libraries), a set of free peer-reviewed portable C++ libraries * Boost (material), a material branded and used by Adidas in the midsoles of shoes. * Boost, a loose term for turbo or supercharger * Boost converter, an electrical circuit variation of a DC to DC converter, which increases (boosts) the voltage * Boosted fission weapon, a type of nuclear bomb that uses a small amount of fusion fuel to increase the rate, and thus yield, of a fission reaction * Boosting (behavioral science), a technique to improve human decisions * Boosting (machine learning), a supervised learning algorithm * Intel Turbo Boost, a technology that enables a processor to run above its base operating frequency * Jump start (vehicle), to start a vehicle * Lorentz boost, a type of Lorentz transformation Arts, entertainment, and media Fictional character ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NumPy
NumPy (pronounced ) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. The predecessor of NumPy, Numeric, was originally created by Jim Hugunin with contributions from several other developers. In 2005, Travis Oliphant created NumPy by incorporating features of the competing Numarray into Numeric, with extensive modifications. NumPy is open-source software and has many contributors. NumPy is fiscally sponsored by NumFOCUS. History matrix-sig The Python programming language was not originally designed for numerical computing, but attracted the attention of the scientific and engineering community early on. In 1995 the special interest group (SIG) ''matrix-sig'' was founded with the aim of defining an array computing package; among its members was Python designer and maintainer Guido van Rossum, who extended Python ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematica
Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in ''Mathematica''. Mathematica 1.0 was released on June 23, 1988 in Champaign, Illinois and Santa Clara, California. Mathematica's Wolfram Language is fundamentally based on Lisp; for example, the Mathematica command Most is identically equal to the Lisp command butlast. There is a substantial literature on the development of computer algebra systems (CAS). __TOC_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and Data and information visualization, data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of R package, software packages, which contain Reusability, reusable code, documentation, and sample data. Some of the most popular R packages are in the tidyverse collection, which enhances functionality for visualizing, transforming, and modelling data, as well as improves the ease of programming (according to the authors and users). R is free and open-source software distributed under the GNU General Public License. The language is implemented primarily in C (programming language), C, Fortran, and Self-hosting (compilers), R itself. Preprocessor, Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noncentral T-distribution
The noncentral ''t''-distribution generalizes Student's t-distribution, Student's ''t''-distribution using a noncentrality parameter. Whereas the central probability distribution describes how a test statistic ''t'' is distributed when the difference tested is null, the noncentral distribution describes how ''t'' is distributed when the null is false. This leads to its use in statistics, especially calculating statistical power. The noncentral ''t''-distribution is also known as the singly noncentral ''t''-distribution, and in addition to its primary use in statistical inference, is also used in Robust statistics, robust modeling for data. Definitions If ''Z'' is a standard normal distribution, normal random variable, and ''V'' is a Chi-squared distribution, chi-squared distributed random variable with ν Degrees of freedom (statistics), degrees of freedom that is independent of ''Z'', then :T=\frac is a noncentral ''t''-distributed random variable with ν degrees of freedom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regularized Incomplete Beta Function
In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral : \Beta(z_1,z_2) = \int_0^1 t^(1-t)^\,dt for complex number inputs z_1, z_2 such that \operatorname(z_1), \operatorname(z_2)>0. The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its symbol is a Greek capital beta. Properties The beta function is symmetric, meaning that \Beta(z_1,z_2) = \Beta(z_2,z_1) for all inputs z_1 and z_2.. Specifically, see 6.2 Beta Function. A key property of the beta function is its close relationship to the gamma function: : \Beta(z_1,z_2)=\frac A proof is given below in . The beta function is also closely related to binomial coefficients. When (or , by symmetry) is a positive integer, it follows from the definition of the gamma function that : \Beta(m,n) =\frac = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution Support (measure theory), supported on the real numbers, discrete or "mixed" as well as Continuous variable, continuous, is uniquely identified by a right-continuous Monotonic function, monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow [0,1] satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from negative infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
