Theory of the Combination of Observations Least Subject to Errors
Part One, Part Two, Supplement
Part of Classics in Applied Mathematics
- Author: Carl Friedrich Gauss
- Translator: G. W. Stewart
- 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.
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