High Quality Content by WIKIPEDIA articles! In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. The phrase test of significance was coined by Ronald Fisher. The use of the word significance in statistics is different from the standard one, which suggests that something is important or meaningful. For example, a study that included tens of thousands of participants might be able to say with very great confidence that people of one race are more intelligent than people of another race by 1/20th of an IQ point. This result would be statistically significant, but the difference is small enough to be utterly unimportant. Many researchers urge that tests of significance should always be...

ISBN: 978-6-1303-2129-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In the mathematical sciences, a stationary process (or strict(ly) stationary process or strong(ly) stationary process) is a stochastic process whose joint probability distribution does not change when shifted in time or space. As a result, parameters such as the mean and variance, if they exist, also do not change over time or position. Stationarity is used as a tool in time series analysis, where the raw data are often transformed to become stationary, for example, economic data are often seasonal and/or dependent on the price level. Processes are described as trend stationary if they are a linear combination of a stationary process and one or more processes exhibiting a trend. Transforming...

ISBN: 978-6-1303-3099-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In the mathematical sciences, a stationary process (or strict(ly) stationary process or strong(ly) stationary process) is a stochastic process whose joint probability distribution does not change when shifted in time or space. As a result, parameters such as the mean and variance, if they exist, also do not change over time or position. Stationarity is used as a tool in time series analysis, where the raw data are often transformed to become stationary, for example, economic data are often seasonal and/or dependent on the price level. Processes are described as trend stationary if they are a linear combination of a stationary process and one or more processes exhibiting a trend. Transforming...

ISBN: 978-6-1305-0031-3
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity. It is an umbrella term that covers the law of large numbers, all central limit theorems and ergodic theorems. If one throws a die once, it is difficult to predict the outcome, but if we repeat this experiment many times, we will see that the number of times each result occurs divided by the number of throws will eventually stabilize towards a specific value. Repeating a series of trials will produce similar, but not identical, results for each series: the average, the standard deviation and...

ISBN: 978-6-1312-4831-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Statistical process control (SPC) is an effective method of monitoring a process through the use of control charts. Control charts enable the use of objective criteria for distinguishing background variation from events of significance based on statistical techniques. Much of its power lies in the ability to monitor both process center and its variation about that center, by collecting data from samples at various points within the process. Variations in the process that may affect the quality of the end product or service can be detected and corrected, thus reducing waste as well as the likelihood that problems will be passed on to the customer. With its emphasis on early detection and...

ISBN: 978-6-1303-1877-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Statistical inference is the process of making conclusions using data that is subject to random variation, for example, observational errors or sampling variation. More substantially, the terms statistical inference, statistical induction and inferential statistics are used to describe systems of procedures which can be used to draw conclusions from every dataset arising from every system affected by random variation. The requirements of such a system of procedures for inference and induction are, initially, that it should produce reasonable answers when applied to simple well-defined situations and that it should be general enough to be applied across a range of situations. The outcome of...

ISBN: 978-6-1312-4789-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Statistical signal processing is an area of Applied Mathematics and Signal Processing that treats signals as stochastic processes, dealing with their statistical properties (e.g., mean, covariance, etc.). Because of its very broad range of application Statistical signal processing is taught at the graduate level in either Electrical Engineering, Applied Mathematics, Pure Mathematics/Statistics, or even Biomedical Engineering and Physics departments around the world, although important applications exist in almost all scientific fields. University of Cambridge for example, offers research within this field in all the departments just mentioned. Данное издание не является...

ISBN: 978-6-1312-4844-3
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Statistical shape analysis is a geometrical analysis from a set of shapes in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathological bone shapes, etc. Some of the important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate average shapes from a (possibly random) sample and to estimate shape variability in a sample. One of the main methods used is principal component analysis. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1304-9499-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In computer science and applied mathematics, particularly the analysis of algorithms, asymptotic analysis is a method of describing limiting behavior. Examples include the performance of algorithms when applied to very large input data, or the behavior of physical systems when they are very large. The simplest example is when we have a function f(n) and wish to describe its properties when n becomes very large. Thus, if f(n) = n2+3n, the term 3n becomes insignificant compared to n2 when n is very large. We say that "f(n) is asymptotically equivalent to n2 as n ? ?" and write f(n) ~ n2. Данное издание не является оригинальным. Книга печатается...

ISBN: 978-6-1311-2091-6
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathemIn mathematics, particularly in calculus, a stationary point is an input to a function where the derivative is zero (equivalently, the gradient is zero): where the function "stops" increasing or decreasing (hence the name). For the graph of a one-dimensional function, this corresponds to a point on the graph where the tangent is parallel to the x-axis. For the graph of a two-dimensional function, this corresponds to a point on the graph where the tangent plane is parallel to the xy plane. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1303-2565-7
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Statistics is the science of making effective use of numerical data relating to groups of individuals or experiments. It deals with all aspects of this, including not only the collection, analysis and interpretation of such data, but also the planning of the collection of data, in terms of the design of surveys and experiments. A statistician is someone who is particularly versed in the ways of thinking necessary for the successful application of statistical analysis. Often such people have gained this experience after starting work in any of a number of fields. Statistical procedures may form the basis of positivist methodology in social sciences such as sociology. There is also a discipline...

ISBN: 978-6-1312-4736-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A statistical model is a set of mathematical equations which describe the behavior of an object of study in terms of random variables and their associated probability distributions. If the model has only one equation it is called a single-equation model, whereas if it has more than one equation, it is known as a multiple-equation model. In mathematical terms, a statistical model is frequently thought of as a pair (Y,P) where Y is the set of possible observations and P the set of possible probability distributions on Y. It is assumed that there is a distinct element of P which generates the observed data. Statistical inference enables us to make statements about which element(s) of this set are...

ISBN: 978-6-1304-9451-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The science of epidemiology has had enormous growth, particularly with charity and government funding. Many researchers have been trained to conduct studies, requiring multiple skills ranging from liaising with clinical staff to the statistical analysis of complex data, such as using Bayesian methods. The role of a Statistical Epidemiologist is to bring the most appropriate methods available to bear on observational study from medical research, requiring a broad appreciation of the underpinning methods and their context of applicability and interpretation. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1305-0188-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, particularly in set theory and model theory, there are at least three notions of stationary set.In mathematics, model theory is the study of (classes of) mathematical structures such as groups, fields, graphs, or even universes of set theory, using tools from mathematical logic. A structure that gives meaning to the sentences of a formal language is called a model for the language. If a model for a language moreover satisfies a particular sentence or theory (set of sentences), it is called a model of the sentence or theory. Model theory has close ties to algebra and universal algebra. This article focuses on finitary first order model theory of infinite structures. Finite model...

ISBN: 978-6-1312-4671-5
Издательство: Книга по требованию
Дата выхода: июль 2011

In recent years a number of authors have found solutions to the Einstein-Maxwell field equations for static gravitational fields with isotropic matter. These solutions may be utilized to model a charged relativistic star as they are matchable to the Reissner-Nordstrom exterior at the boundary. It is for this reason that many investigators use a variety of techniques to attain exact solutions. This book provides exact solutions to the isotropic Einstein-Maxwell system that model the interior of relativistic stars. The field equations are transformed to simpler forms; the integration of the system is reduced to solving the condition of pressure isotropy. New classes of solutions of linearly independent functions are obtained in terms of...

ISBN: 978-3-6392-6089-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Statistical models of the sources of data and typical problem formulation: 1. Sampling from a finite population 2. Measuring observational error and refining procedures 3. Studying statistical relations Generating informative data using optimization and randomization while measuring and controlling observational error. Optimization reduces the cost of data while meeting statistical needs, while randomization warrants reliable inferences: 1. Design of experiments to determine treatment effects. 2. Survey sampling to describe natural populations Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1312-4898-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A statistical parameter is a parameter that indexes a family of probability distributions. It can be regarded as a numerical characteristic of a population or a model. Among parameterized families of distributions are the normal distributions, the Poisson distributions, the binomial distributions, and the exponential distributions. The family of normal distributions has two parameters, the mean and the variance: if these are specified, the distribution is known exactly. The family of chi-squared distributions, on the other hand, has only one parameter, the number of degrees of freedom. Данное издание не является оригинальным. Книга печатается...

ISBN: 978-6-1312-4806-1
Издательство: Книга по требованию
Дата выхода: июль 2011

For environmental data classical statistical analysis are often not useful which makes it necessary to find new methods to solve the resulting problems. To make it easier to understand the problems, and the solutions, for environmental data, this book tries to avoid mathematical formulae as much as possible. Therfore many things are explained with graphics. For creating the graphs R and the Kola dataset (consists of observations of the Kola Ecogeochemistry Project) were used. This dataset consists of more than 60 chemical elements of northern Finland, Norway and Russia. At the end of the book the functions (for creating the plots) are descriped. This book was written together with P. Filzmoser who wrotes "Statistical Data Analysis...

ISBN: 978-3-6390-2679-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem (also Stefan task) is a particular kind of boundary value problem for a partial differential equation (PDE), adapted to the case in which a phase boundary can move with time. Hence, Stefan problems are examples of moving boundary problems. It is named after Jozef Stefan, the Slovene physicist who introduced the general class of such problems around 1890, in relation to problems of ice formation. This question had been considered earlier, in 1831, by Lame and Clapeyron. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1312-4981-5
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Stefan Kaczmarz (born 1895 in Lviv (Lemberg), Galicia, Austria-Hungary (now Ukraine) - 1940) was a Polish mathematician. His Kaczmarz method provided the basis for many modern imaging technologies, including the CAT scan. Kaczmarz was an adjunct professor of mechanics at the Lwow Polytechnic where he collaborated with Stefan Banach. Kaczmarz, along with many other members of the Polish intelligentsia, was rounded up by the NKVD after the Soviet invasion of Poland in 1939. He, and others who were declared to be the enemies of the Soviet regime, were murdered by the NKVD on orders from the Politburo in 1940 in the Katy? massacre. Данное издание не является...

ISBN: 978-6-1311-1168-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Stefan Mazurkiewicz (September 25, 1888 in Warsaw, then Russian Empire – June 19, 1945, Grodzisk Mazowiecki, Poland) was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wac?aw Sierpi?ski and a member of the Polish Academy of Learning (PAU). His students included Karol Borsuk, Bronis?aw Knaster, Kazimierz Kuratowski, Stanis?aw Saks, and Antoni Zygmund. For a time Mazurkiewicz was a professor ath the University of Paris, however he spent most of his career as a professor at the University of Warsaw. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1311-6647-1
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Stefan Banach (1892–1945) was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. A self-taught mathematics prodigy, Banach was the founder of modern functional analysis and a founder of the Lwow School of Mathematics. Among his most prominent achievements was the 1932 book, Theorie des operations lineaires (Theory of Linear Operations), the first monograph on the general theory of linear-metric space. Notable mathematical concepts named after Banach include the Banach–Tarski paradox, Hahn–Banach theorem, Banach–Steinhaus theorem, Banach-Mazur game and Banach space. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1311-1153-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In numerical analysis, Steffensen's method is a root-finding method. It is similar to Newton's method and it also achieves quadratic convergence, but it does not use derivatives. The method is named after Johan Frederik Steffensen.Numerical analysis is the study of algorithms that use numerical values (as opposed to general symbolic manipulations) for the problems of continuous mathematics (as distinguished from discrete mathematics). One of the earliest mathematical writings is the Babylonian tablet YBC 7289, which gives a sexagesimal numerical approximation of sqrt{2}, the length of the diagonal in a unit square. Being able to compute the sides of a triangle (and hence, being able to compute...

ISBN: 978-6-1312-4999-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In geometry, a Steiner chain is a set of n circles, all of which are tangent to two given non-intersecting circles (blue and red in Figure 1), where n is finite and each circle in the chain is tangent to the previous and next circles in the chain. In the usual closed Steiner chains, the first and last (nth) circles are also tangent to each other; by contrast, in open Steiner chains, they need not be. The given circles ? and ? do not intersect, but otherwise are unconstrained; the smaller circle may lie completely inside or outside of the larger circle. If these cases, the centers of Steiner-chain circles lie on an ellipse or a hyperbola, respectively. Данное издание не...

ISBN: 978-6-1312-5356-0
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Steinhaus–Johnson–Trotter algorithm or Johnson–Trotter algorithm is an algorithm that generates permutations by transposing elements.The algorithm is set up with the idea that only one set of neighbors needs to swap positions and that there need only be one swap to generate the next permutation. To accommodate this, there needs to be an extra data element added: direction of mobility (ie direction of the swap). This direction is either left or right, but is initialized to the left.An integer is said to be mobile if, in the direction of its mobility, the nearest integer is less than the current integer....

ISBN: 978-6-1312-5385-0
Издательство: Книга по требованию
Дата выхода: июль 2011