Using this normal law as a generic model for errors in the experiments, Gauss formulates what is now known as the non-linear weighted least squares (NWLS) method. Einflüsse der Zugabe ausgewählter Glasbestandteile auf die optische Dispersion eines speziellen Basisglases. For normally distributed vectors, see, "Bell curve" redirects here. Hoel (1947) "Introduction to mathematical statistics" and A.M. Measures of size of living tissue (length, height, skin area, weight); Certain physiological measurements, such as blood pressure of adult humans. Mood (1950) "Introduction to the theory of statistics". In Lichtwellenleitern gibt es außerdem Polarisationsmodendispersion. Dispersion und Gruppengeschwindigkeit . Dispersion bedeutet im Allgemeinen "Zerstreuung" oder "Verteilung". Kramers-Heisenbergsche Dispersionsformel, Herzbergsche Dispersionsformel (für den visuellen Bereich, Auch magnetische Linsen etwa eines Elektronenmikroskops zeigen Dispersion in Abhängigkeit von der Geschwindigkeit der Elektronen. Die einzelnen Substanzen können fest, flüssig oder gasförmig sein. c(L,d) c(f,d) Schwerewellen . von lateinisch: dispergere - auseinanderstreuen, zerstreuen This is not the case, however, with the total variance of the mean: As the unknown variance increases, the total variance of the mean will increase proportionately, and we would like to capture this dependence. ", "Rational Chebyshev Approximations for the Error Function", "On the optimal rates of convergence for nonparametric deconvolution problems", "Mémoire sur la probabilité des causes par les événements", "The Ziggurat Method for Generating Random Variables", "On Lines and Planes of Closest Fit to Systems of Points in Space", "Wilhelm Lexis: The Normal Length of Life as an Expression of the "Nature of Things, "Mathematical Statistics in the Early States", "De Moivre on the Law of Normal Probability", "Better Approximations to Cumulative Normal Functions", Handbook of mathematical functions with formulas, graphs, and mathematical tables, https://en.wikipedia.org/w/index.php?title=Normal_distribution&oldid=980625524, Location-scale family probability distributions, Articles with unsourced statements from June 2011, Articles with unsourced statements from June 2010, Articles with unsourced statements from May 2020, Creative Commons Attribution-ShareAlike License, The probability that a normally distributed variable, The family of normal distributions not only forms an, The absolute value of normalized residuals, |. This page was last edited on 27 September 2020, at 15:10. ... of obtaining the observed experimental results. —, "My custom of terming the curve the Gauss–Laplacian or, Besides those specifically referenced here, such use is encountered in the works of, Geary RC(1936) The distribution of the "Student's" ratio for the non-normal samples". Edward L. Melnick and Aaron Tenenbein, "Misspecifications of the Normal Distribution", De Moivre, Abraham (1733), Corollary I – see, modified Bessel function of the second kind, Maximum likelihood § Continuous distribution, continuous parameter space, Gaussian function § Estimation of parameters, Error function#Approximation with elementary functions, Normally distributed and uncorrelated does not imply independent, Sum of normally distributed random variables, "List of Probability and Statistics Symbols", "Wolfram|Alpha: Computational Knowledge Engine", "Maximum Entropy Autoregressive Conditional Heteroskedasticity Model", "On three characterisations of the normal distribution", "Kullback Leibler (KL) Distance of Two Normal (Gaussian) Probability Distributions", "Stat260: Bayesian Modeling and Inference: The Conjugate Prior for the Normal Distribution", "Normal Approximation to Poisson Distribution", "A Characterization of the Normal Distribution", "Chapter 6: Frequency and Regression Analysis of Hydrologic Data", "Earliest uses... (entry STANDARD NORMAL CURVE)", "Earliest Uses of Symbols in Probability and Statistics", "Earliest Known Uses of Some of the Words of Mathematics", "Error, law of error, theory of errors, etc.
[note 5] It was Laplace who first posed the problem of aggregating several observations in 1774,[69] although his own solution led to the Laplacian distribution. Dies ist die Grundlage vieler Spektralapparate. Der Effekt führt zu Laufzeitverzerrungen bei breitbandigen Signalen (zum Beispiel in Form von flacheren Impulsflanken) und kann durch geeignete Isolierstoffe vermieden werden. [73], In the middle of the 19th century Maxwell demonstrated that the normal distribution is not just a convenient mathematical tool, but may also occur in natural phenomena:[74] "The number of particles whose velocity, resolved in a certain direction, lies between x and x + dx is, Since its introduction, the normal distribution has been known by many different names: the law of error, the law of facility of errors, Laplace's second law, Gaussian law, etc. Darüber hinaus gibt es noch zahlreiche weitere Dispersionsformeln[2], z. Bitte logge Dich ein, um diesen Artikel zu bearbeiten. Helmholtz-Ketteler-Drude-Dispersionsformel. Chemie, Dass Dispersionen Wasserdampf weniger gut aufnehmen und wieder abgeben können, liegt an der Filmbildung. … [78], This article is about the univariate probability distribution. [71], It is of interest to note that in 1809 an Irish mathematician Adrain published two derivations of the normal probability law, simultaneously and independently from Gauss. Die Sellmeier-Gleichung dagegen versucht, den empirisch ermittelten Verlauf des Brechungsindex $ n $ über die Wellenlänge $ \lambda $ genau wiederzugeben. Thus, we should logically think of our priors in terms of the sufficient statistics just described, with the same semantics kept in mind as much as possible. Bei den meisten transparenten Stoffen steigt im sichtbaren Bereich der Brechungsindex mit der Frequenz an, Glas bricht blaues Licht stärker als rotes. Normale und anomale Dispersion . Um diesen Artikel zu kommentieren, melde Dich bitte an. Eine positive Ableitung des Brechungsindex nach der Frequenz der Welle ($ \text{d}n / \text{d}\omega \,>\, 0 $) ist gleichbedeutend mit einer negativen Ableitung nach der Wellenlänge ($ \text{d}n / \text{d}\lambda \,<\, 0 $). [70] Finally, it was Laplace who in 1810 proved and presented to the Academy the fundamental central limit theorem, which emphasized the theoretical importance of the normal distribution.
Der Effekt ist keine spezielle Eigenschaft dieses Farbstoffs, vielmehr tritt er immer in Wellenlängenbereichen nahe einer starken Absorption auf. Their sum and difference is distributed normally with mean zero and variance two: Either the mean, or the variance, or neither, may be considered a fixed quantity. Englisch: dispersion. Supplement to the Journal of the Royal Statistical Society 3 (2): 178–184, Lukas E (1942) A characterization of the normal distribution.

In der Physik beschreibt Dispersion die Abhängigkeit einer physikalischen Größe von der Wellenlänge bzw. Der Text dieser Seite basiert auf dem Artikel. Klicke hier, um einen neuen Artikel im DocCheck Flexikon anzulegen. Physik. Kosmische Diamanten entstehen bei gigantischen planetaren Kollisionen, Treffen der Generationen im Herzen der Galaxis, CHEOPS Weltraumteleskop: Einer der extremsten Planeten im Universum, Atombillard mit Röntgenstrahlen: Blick ins Innere von Molekülen, Erste Messungen der Strahlendosis auf dem Mond, Historischer Himmel: Halbes Jahrhundert Potsdamer Sonnenforschung digital, Galaxien gefangen im Netz eines supermassereichen schwarzen Lochs.

Erste Daten von Solar Orbiter online veröffentlicht. Normal dispersion, for example, leads to a lower group velocity of higher-frequency components, and thus to a positive chirp, whereas anomalous dispersion creates negative chirps.

Regression problems – the normal distribution being found after systematic effects have been modeled sufficiently well.