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Why the Normal Distribution

Published online by Cambridge University Press:  11 August 2014

R. H. Daw
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Extract

It has been said that everybody believes in the Law of Errors (i.e. the Normal distribution), the experimenters because they think it is a mathematical theorem and the mathematicians because they think it is an experimental fact. Text-books on statistics often seem to produce the Normal distribution as the conjurer produces a rabbit from a hat and the actuarial student, who should be something of both mathematician and experimenter, is frequently somewhat mystified as to why such an apparently complicated distribution function as

Fig. 1. The Normal distribution

(see Fig. 1) is suddenly introduced and given such prominence.

Type
Research Article
Information
Journal of the Staple Inn Actuarial Society , Volume 18 , Issue 1 , October 1966 , pp. 2 - 15
Copyright
Copyright © Institute of Actuaries Students' Society 1966

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References

REFERENCES

Airy, G. B. (1879). On the algebraic and numerical theory of errors of observation and the combination of observations (3rd edition). London: Macmillan & Co. Google Scholar
Archibald, R. C. (1926). A rare pamphlet of Moivre and some of his discoveries. Isis, 8, 671.Google Scholar
Birnbaum, Z. W. (1953). Distribution-free tests of fit for continuous distribution functions. Ann. Math. Statist., 24, 1.CrossRefGoogle Scholar
Box, G. E. P. (1953). Non-normality and tests on variances. Biometrika, 40, 318.Google Scholar
Brunt, D. (1931). The combination of observations. Cambridge University Press.Google Scholar
Cramer, H. (1946). Mathematical methods of statistics, Princeton University Press.Google Scholar
Davies, O. L. (Ed.) (1956). The design and analysis of industrial experiments. London: Oliver & Boyd.Google Scholar
De Moivre, A. (1738). The Doctrine of Chances (2nd edition).Google Scholar
De Morgan, A. (1838) An essay on probabilities and on their application to life contingencies and insurance offices. London.Google Scholar
Gayen, A. K. (1949). The distribution of Student's t in random samples of any size drawn from non-normal universes. Biometrika, 36, 353.Google Scholar
Gayen, A. K. (1950a). The distribution of the variance ratio in random samples of any size drawn from non-normal universes. Biometrika, 37, 236.Google Scholar
Gayen, A. K. (1950b). Significance of difference between the means of two non-normal samples. Biometrika, 37, 399.Google Scholar
Geary, R. C. (1947). Testing for normality. Biometrika, 34, 209.CrossRefGoogle ScholarPubMed
Irwin, J. O. (1927). On the frequency distribution of the means of samples from a population having any law of frequency with finite moments with special reference to Pearson's Type II. Biometrika, 19, 225.Google Scholar
Jeffreys, H. (1938). The law of error and the combination of observations. Phil. Trans. Roy. Soc. A, 237, 231.Google Scholar
Jeffreys, H. (1939). Theory of Probability. Oxford University Press.Google Scholar
Kendall, M. G. (1951). The advanced theory of statistics, 2. London: Griffin.Google Scholar
Kendall, M. G. and Stuart, A. (1963). The advanced theory of statistics, 1. London: Griffin.Google Scholar
Pearson, E. S. (1965) Studies in the history of probability and statistics XIV. Some incidents in the early history of biometry and statistics, 1890–1894. Biometrika, 52, 3.CrossRefGoogle ScholarPubMed
Pearson, E. S. and Hartley, H. O. (1954). Biometrika tables for statisticians. Cambridge University Press.Google Scholar
*Pearson, K. (1894). Contributions to the mathematical theory of evolution. Phil. Trans. Roy. Soc., A, 185, 71.Google Scholar
*Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine, 50, 157.Google Scholar
Quenouille, M. H. (1950). Introductory statistics. London: Butterworths.Google Scholar
Shapiro, S. S. and Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52, 591.Google Scholar
Smith, D. E. (1929). A source book in mathematics. New York & London: McGraw Hill.Google Scholar
Walker, H. M. (1929). Studies in the history of statistical method. Baltimore: Williams and Wilkins.Google Scholar
Whittaker, E. and Robinson, G. (1949). The calculus of observations. London: Blackie.Google Scholar
Yule, G. U. and Kendall, M. G. (1950). An introduction to the theory of statistics. London: Griffin.Google Scholar
* These papers are reprinted in Karl Pearson's early statistical papers. Cambridge University Press, 1948.Google Scholar