Theory of the Combination of Observations Least Subject to Errors
Theory of the Combination of Observations Least Subject to Errors
G. W. Stewart
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GBPIn 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.
Product details
April 1995Paperback
9780898713473
253 pages
260 × 190 × 14 mm
0.498kg
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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.
