Book contents
- Frontmatter
- Contents
- Editor's foreword
- Preface
- Part I Principles and elementary applications
- 1 Plausible reasoning
- 2 The quantitative rules
- 3 Elementary sampling theory
- 4 Elementary hypothesis testing
- 5 Queer uses for probability theory
- 6 Elementary parameter estimation
- 7 The central, Gaussian or normal distribution
- 8 Sufficiency, ancillarity, and all that
- 9 Repetitive experiments: probability and frequency
- 10 Physics of ‘random experiments’
- Part II Advanced applications
- Appendix A Other approaches to probability theory
- Appendix B Mathematical formalities and style
- Appendix C Convolutions and cumulants
- References
- Bibliography
- Author index
- Subject index
7 - The central, Gaussian or normal distribution
from Part I - Principles and elementary applications
Published online by Cambridge University Press: 05 September 2012
- Frontmatter
- Contents
- Editor's foreword
- Preface
- Part I Principles and elementary applications
- 1 Plausible reasoning
- 2 The quantitative rules
- 3 Elementary sampling theory
- 4 Elementary hypothesis testing
- 5 Queer uses for probability theory
- 6 Elementary parameter estimation
- 7 The central, Gaussian or normal distribution
- 8 Sufficiency, ancillarity, and all that
- 9 Repetitive experiments: probability and frequency
- 10 Physics of ‘random experiments’
- Part II Advanced applications
- Appendix A Other approaches to probability theory
- Appendix B Mathematical formalities and style
- Appendix C Convolutions and cumulants
- References
- Bibliography
- Author index
- Subject index
Summary
My own impression … is that the mathematical results have outrun their interpretation and that some simple explanation of the force and meaning of the celebrated integral … will one day be found … which will at once render useless all the works hitherto written.
Augustus de Morgan (1838)Here, de Morgan was expressing his bewilderment at the ‘curiously ubiquitous’ success of methods of inference based on the Gaussian, or normal, ‘error law’ (sampling distribution), even in cases where the law is not at all plausible as a statement of the actual frequencies of the errors. But the explanation was not forthcoming as quickly as he expected.
In the middle 1950s the writer heard an after-dinner speech by Professor Willy Feller, in which he roundly denounced the practice of using Gaussian probability distributions for errors, on the grounds that the frequency distributions of real errors are almost never Gaussian. Yet in spite of Feller's disapproval, we continued to use them, and their ubiquitous success in parameter estimation continued. So, 145 years after de Morgan's remark, the situation was still unchanged, and the same surprise was expressed by George Barnard (1983): ‘Why have we for so long managed with normality assumptions?’
Today we believe that we can, at last, explain (1) the inevitably ubiquitous use, and (2) the ubiquitous success, of the Gaussian error law.
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- Probability TheoryThe Logic of Science, pp. 198 - 242Publisher: Cambridge University PressPrint publication year: 2003
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