Abstract
The ‘skewness’ of a distribution, a poorly-defined term, is conventionally deemed to be invariant under linear transformations. A comparison is made of three criteria of it: the sign of odd central moments; the several relationships of the mean, the median and the mode; and asymmetry proper which is the set of ratios of the probability densities of all pairs of points equidistant above and below some arbitrary point, usually the principal mode. Some useful general relationships are discussed. The skeness of convolutions is briefly discussed. A class of distributions is identified for which the skewness of the minimum ofk competing processes is independent ofk. It has importance in the parametric study of survivorship.
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Murphy, E. A., Trojak, J. L., Hou, W., and Rohde, C. A.: ‘The bingo model of survivorship. 1. Probabilistic aspects’,Amer. J. Med. Genet., in press.
Murphy, E. A.:The Logic of Medicine, Johns Hopkins University Press, Baltimore, 1976.
Murphy, E. A.:Probability in Medicine. Johns Hopkins University Press, Baltimore, 1979.
MacFarlane, R. G.: ‘An enzyme cascade in the blood clotting mechanism and its function as a biological amplifier’,Nature 202, (1964) 498–499.
Harris, H. and Smith, C. A. B.: ‘The sib-sib age of onset correlation among individuals suffering from a hereditary syndrome produced by more than one gene’,Ann. Eugen. 14, (1949) 309–318.
Nordling, C. O.: ‘A new theory on the cancer-inducing mechanism’,Br. J. Cancer 7, (1953) 68–72.
Armitage, P. and Doll, R.: ‘Stochastic models for carcinogenesis’, in Neyman, J. (ed.),Proceedings of 4th Berkeley Symposium, Mathematical Statistics and Probability, IV: Biology and Problems of Health, University of California Press, Berkeley, 1961.
Mustard, J. F., Murphy, E. A., Rowsell, H. C., and Downie, H. G.: ‘Factors influencing thrombus formationin vivo’.Amer. J. Med. 33, (1962) 621–647.
Begent, N. and Born, G. V. R.: ‘Growth ratein vivo of platelet thrombi, produced by iontophoresis of ADP, as a function of mean blood flow velocity’,nature,227, (1970) 926–930.
Snedecor, G. W., and Cochran, W. G.:Statistical Methods, Seventh edition, Iowa State University Press, Ames, Iowa, 1980.
Kendall, M. G., and Stuart, A.:The Advanced Theory of Statistics, Vol. II, Chapter 17, Haffner, New York, 1961.
Groeneveld, R. A. and Meeden, G.: ‘The mode, median and mean inequality’,Amer. Stat. 31, (1977) 121–122.
Armitage, P. and Doll, R.: ‘The age distribution of cancer and a multi-stage theory of carcinogenesis’,Br. J. Cancer,8, (1954) 1–12.
Knudson, A. G.: ‘Genetic and environmental interaction in the origin of human cancer inGenetics of Human Cancer’, in Progress in Cancer Research and Therapy Vol. 3 edited by J. J. Mulvihill, R. W. Miller, and J. F. Fraumeni, Raven, New York, 1977.
Murphy E. A.: ‘Hereditary polyposis II. Genetic counselling’,Johns Hop. Med. J.,145, (1979) 177–186.
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The research for this paper was supported by Grant AG01334 of The National Institutes of Health.