On the mean character and variance of a ranked individual, and on the mean and variance of the intervals between ranked individuals - Part II Case of certain skew curves
成果类型：
Article
署名作者：
Pearson, K
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2333800
发表日期：
1932
页码：
203279
关键词：
摘要：
Analytical results are dc- . rived and illustrated numerically for samples from exponential and allied frequency curves, which are important as describing the random distribution of the occurrence of events in time or space. The correlation between adjacent rank-variants is high, but that between rank-intervals is small, and for many purposes negligible. The partial correlation of any 2 rank-variates or rank-intervals for a constant rank-variate or rank-interval lying between them is 0. The order of the standard deviations of rank-intervals is much the same as that of the intervals themselves. There is equality for the exponential curve, and this property extends approximately for some distance on each side of it. Gal-ton''s ratio, 2 to 1, for the ratio of the first rank-interval to the second for the end of the curve with lesser frequency is approximately true for many curves. In samples from a curve of finite range the correlations of adjacent rank-intervals are negative; in those from one with unlimited range they are positive. When there is much predominance of mediocrity the interval between the first and second ranks may be 10 or more times the interval between mediocre individuals. This is but a special illustration of the great principle that differences in physical or mental ability between specially able individuals are much greater than those between ordinary individuals. Several characteristics of the so-called genius are involved in this principle. The curves dealt with are widely spread over the fit, fit plane. The properties found for them are likely to hold for curves with their [beta]1, [beta]2 not far from the biquadratic, and some may possibly hold for all continuous frequency curves.
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