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Theory of the Combination of Observations Least Subject to Errors

Theory of the Combination of Observations Least Subject to Errors
Part One, Part Two, Supplement

Part of Classics in Applied Mathematics

  • Date Published: April 1995
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898713473

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  • In the 1820s Gauss published two memoirs on least squares, which contain his final, definitive treatment of the area along with a wealth of material on probability, statistics, numerical analysis, and geodesy. These memoirs, originally published in Latin with German Notices, have been inaccessible to the English-speaking community. Here for the first time they are collected in an English translation. For scholars interested in comparisons the book includes the original text and the English translation on facing pages. More generally the book will be of interest to statisticians, numerical analysts, and other scientists who are interested in what Gauss did and how he set about doing it. An Afterword by the translator, G. W. Stewart, places Gauss's contributions in historical perspective.

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    Product details

    • Date Published: April 1995
    • format: Paperback
    • isbn: 9780898713473
    • length: 253 pages
    • dimensions: 260 x 190 x 14 mm
    • weight: 0.498kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    part one
    part or mean value of the error
    The mean square error as a measure of uncertainty
    Mean error, weight and precision
    Effect of removing the constant part
    Interpercentile ranges and probable error
    properties of the uniform, triangular, and normal distribution
    Inequalities relating the mean error and interpercentile ranges
    The fourth moments of the uniform, triangular, and normal distributions
    The distribution of a function of several errors
    The mean value of a function of several errors
    Some special cases
    Convergence of the estimate of the mean error
    the mean error of the estimate itself
    the mean error of the estimate for the mean value
    Combining errors with different weights
    Overdetermined systems of equations
    the problem of obtaining the unknowns as combinations of observations
    the principle of least squares
    The mean error of a function of quantities with errors
    The regression model
    The best combination for estimating the first unknown
    The weight of the estimate
    estimates of the remaining unknowns and their weights
    justification of the principle of least squares
    The case of a single unknown
    the arithmetic mean. Pars Posterior/part two
    part two
    Part I
    Part II.

  • Author

    Carl Friedrich Gauss

    Translator

    G. W. Stewart

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