Gauss Error Laws
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Error Propagation Chemistry
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propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate to the combination of variables in the function. error propagation inverse The uncertainty u can be expressed in a number of ways. It may be defined by the
Error Propagation Reciprocal
absolute error Δx. Uncertainties can also be defined by the relative error (Δx)/x, which is usually written as a percentage. Most commonly, the uncertainty on
Error Propagation Average
a quantity is quantified in terms of the standard deviation, σ, the positive square root of variance, σ2. The value of a quantity and its error are then expressed as an interval x ± u. If the statistical probability distribution of the http://onlinelibrary.wiley.com/doi/10.1002/0471667196.ess1408.pub2/pdf variable is known or can be assumed, it is possible to derive confidence limits to describe the region within which the true value of the variable may be found. For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are ± one standard deviation from the value, that is, there is approximately a 68% probability that the true value lies in the region x ± σ. If the uncertainties are correlated then covariance must be taken into account. Correlation https://en.wikipedia.org/wiki/Propagation_of_uncertainty can arise from two different sources. First, the measurement errors may be correlated. Second, when the underlying values are correlated across a population, the uncertainties in the group averages will be correlated.[1] Contents 1 Linear combinations 2 Non-linear combinations 2.1 Simplification 2.2 Example 2.3 Caveats and warnings 2.3.1 Reciprocal 2.3.2 Shifted reciprocal 3 Example formulas 4 Example calculations 4.1 Inverse tangent function 4.2 Resistance measurement 5 See also 6 References 7 Further reading 8 External links Linear combinations[edit] Let { f k ( x 1 , x 2 , … , x n ) } {\displaystyle \ ρ 5(x_ ρ 4,x_ ρ 3,\dots ,x_ ρ 2)\}} be a set of m functions which are linear combinations of n {\displaystyle n} variables x 1 , x 2 , … , x n {\displaystyle x_ σ 7,x_ σ 6,\dots ,x_ σ 5} with combination coefficients A k 1 , A k 2 , … , A k n , ( k = 1 … m ) {\displaystyle A_ σ 1,A_ σ 0,\dots ,A_ ρ 9,(k=1\dots m)} . f k = ∑ i n A k i x i or f = A x {\displaystyle f_ ρ 5=\sum _ ρ 4^ ρ 3A_ ρ 2x_ ρ 1{\text{ or }}\mathrm ρ 0 =\mathrm σ 9 \,} and let the variance-covariance matrix on x be denoted by Σ x {\displaystyle \mathrm {\Sigma ^ σ 1} \,} . Σ x = ( σ 1 2 σ 12 σ 13 ⋯ σ 12 σ 2 2 &
von GoogleAnmeldenAusgeblendete FelderBooksbooks.google.de - Suitable for graduate students in chemical physics, statistical physics, https://books.google.com/books?id=h4LEDAAAQBAJ&pg=PA339&lpg=PA339&dq=gauss+error+laws&source=bl&ots=7OXqytLwSh&sig=Z5Q_ZG0cEjhesmtYD7SQ-LNUovA&hl=en&sa=X&ved=0ahUKEwjJ_8fdzNjPAhUCqh4KHcpJCGMQ6AEIRjAG and physical chemistry, this text develops an innovative, http://www.sciencedirect.com/science/article/pii/S0375960105013630 probabilistic approach to statistical mechanics. The treatment employs Gauss's principle and incorporates Bose-Einstein and Fermi-Dirac statistics to provide a powerful tool...https://books.google.de/books/about/Statistical_Physics.html?hl=de&id=h4LEDAAAQBAJ&utm_source=gb-gplus-shareStatistical PhysicsMeine BücherHilfeErweiterte BuchsucheE-Book kaufen - 22,72 €Nach Druckexemplar suchenAmazon.deBuch.deBuchkatalog.deLibri.deWeltbild.deIn Bücherei error propagation suchenAlle Händler»Statistical Physics: A Probabilistic ApproachBernard H. LavendaCourier Dover Publications, 01.08.2016 - 384 Seiten 0 Rezensionenhttps://books.google.de/books/about/Statistical_Physics.html?hl=de&id=h4LEDAAAQBAJSuitable for graduate students in chemical physics, statistical physics, and physical chemistry, this text develops an innovative, probabilistic approach to statistical mechanics. gauss error laws The treatment employs Gauss's principle and incorporates Bose-Einstein and Fermi-Dirac statistics to provide a powerful tool for the statistical analysis of physical phenomena. The treatment begins with an introductory chapter on entropy and probability that covers Boltzmann's principle and thermodynamic probability, among other topics. Succeeding chapters offer a case history of black radiation, examine quantum and classical statistics, and discuss methods of processing information and the origins of the canonical distribution. The text concludes with explorations of statistical equivalence, radiative and material phase transitions, and the kinetic foundations of Gauss's error law. Bibliographic notes complete each chapter. Voransicht des Buches » Was andere dazu sagen-Rezension schreibenEs wurden keine Rezensionen gefunden.Ausgewählte Seit
Please note that Internet Explorer version 8.x will not be supported as of January 1, 2016. Please refer to this blog post for more information. Close ScienceDirectSign inSign in using your ScienceDirect credentialsUsernamePasswordRemember meForgotten username or password?Sign in via your institutionOpenAthens loginOther institution loginHelpJournalsBooksRegisterJournalsBooksRegisterSign inHelpcloseSign in using your ScienceDirect credentialsUsernamePasswordRemember meForgotten username or password?Sign in via your institutionOpenAthens loginOther institution login Purchase Help Direct export Export file RIS(for EndNote, Reference Manager, ProCite) BibTeX Text RefWorks Direct Export Content Citation Only Citation and Abstract Advanced search JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page. JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page. This page uses JavaScript to progressively load the article content as a user scrolls. Click the View full text link to bypass dynamically loaded article content. View full text Physics Letters AVolume 348, Issues 3–6, 2 January 2006, Pages 89–93 κ-generalization of Gauss' law of errorTatsuaki Wadaa, , , Hiroki Suyarib, , a Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki 316-8511, Japanb Department of Information and Image Sciences, Chiba University, Chiba 263-8522, JapanReceived 27 May 2005, Revised 9 August 2005, Accepted 9 August 2005, Available online 6 September 2005Communicated by C.R. DoeringAbstractBased on the κ-deformed functions (κ-exponential and κ-logarithm) and associated multiplication operation (κ-product) introduced by Kaniadakis [Phys. Rev. E 66 (2002) 056125], we present another one-parameter generalization of Gauss' law of error. The likelihood function in Gauss' law of error is generalized by means of the κ-product. This κ-generalized maximum likelihood principle leads to the so-called κ-Gaussian distributions.PACS02.50.Cw; 05.20.-y; 06.20.DkKeywordsGauss' law of error; κ-deformed function; κ-productCorresponding author.Copyright © 2005 Elsevier B.V. All rights reserved. ElsevierAbout ScienceDirectRemote accessShopping cartContact and supportTerms and conditionsPrivacy policyCookies are used by this site.