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The Use of Probability Paper for the Graphical Analysis of Polymodal Frequency Distributions

Published online by Cambridge University Press:  11 May 2009

J. P. Harding
J. P. Harding
Affiliation:
British Museum, Natural History
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Extract

The mathematical analysis of bimodal distributions is very complex. Karl Pearson (1894) investigated the problem and developed equations for the purpose; but found them unsolvable as the ‘majority [of the relations] lead to exponential equations the solution of which seems more beyond the wit of man than that of a numerical equation even of the ninth order’. He did indeed evolve an equation of this order and used it to analyse a few bimodal distributions, but the arithmetic involved was very laborious. Later he (Pearson, 1914) gives a table for ‘Constants of normal curve from moments of tail about stump ’which, as he describes in the introduction, occasionally permits a rough analysis of a distribution which is known to be bimodal. This method is much more rapid than the solution of the nonic equation, but ‘owing to the paucity of material in tails and corresponding irregularity there will be large probable errors’. Gottschalk (1948) discusses the question and shows that inthe special case where the bimodal distribution is symmetrical comparatively simple solutions can be found.

Type
Research Article
Information
Journal of the Marine Biological Association of the United Kingdom , Volume 28 , Issue 1 , June 1949 , pp. 141 - 153
Copyright
Copyright © Marine Biological Association of the United Kingdom 1949

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References

REFERENCES

Buchanan-Wollaston, H. J. & Hodgson, W. C. 1929. A new method of treating frequency curves in fishery statistics, with some results. Journ. Conseil Int. Explor. Mer, Copenhagen, Vol. 4, pp. 207–25.CrossRefGoogle Scholar
Doust, J. F. & Josephs, H. J. 1941–1942. A simple introduction to the use of statistics in telecommunications engineering. Post Office Eng. Journ., Vol 34, pp. 36–41,79–84, 139–44 and 173–8.Google Scholar
Ford, E., 1928. Herring investigations at Plymouth. III. The Plymouth winter fishery during the seasons 1924–25, 1925–6 and 1926–7. Journ. Mar. Biol. Assoc., Vol. 15, pp. 279–304.CrossRefGoogle Scholar
Gottschalk, V. H., 1948. Symmetrical bi-modal frequency curves. Journ. Franklin Inst. Philadelphia, Vol. 245, pp. 245–52.CrossRefGoogle ScholarPubMed
Hazen, A., 1913. Storage to be provided in impounding reservoirs for municipal water supply. Proc. Amer. Soc. Civil Eng., Vol. 39, pp. 1943–2044.Google Scholar
Levi, F., 1946. Graphical solutions for statistical problems. The Engineer, London, Vol. 182, pp. 338–40 and 362–4.Google Scholar
Pearson, K., 1894. Contribution to the mathematical theory of evolution. Phil. Trans. Roy. Soc., A, Vol. 185, pp. 71–110.Google Scholar
Pearson, K. 1914. Tables for statisticians and biometricians, Part I. Cambridge.Google Scholar
Rissik, H., 1941. Probability graph paper and its engineering applications. The Engineer, London, Vol. 172, pp. 276–82 and 296–8.Google Scholar