摘要:

Equations relating the statistics of a linear, composite, bivariate, normal distribution with those of the component distributions are derived for two types of data; first, for the special (ideal) case when the means represented by the samples correspond to the points of the linear continuum, and the proportions of the component populations remain constant and, second, for the practical case when the point set representing the means of the component distributions from which the samples have been drawn differs from the linear continuum, and the proportions or densities of the component populations vary along the line of relation. The results show that, if the component populations are normal and the variances and correlation coefficient in the component populations are constant, we can calculate at most only two of the parameters of the component populations from the composite data. We can, however, always calculate the values of the slope of the line of relation and the vertical variance around this line irrespective of the functional forms of the component populations, providing the means of the latter are collinear and provided also that the data can be separated into subgroups corresponding to single populations. The use of the equations is illustrated by means of a composite distribution constructed from a known component distribution.

ISSN:1923-4287    

DOI:10.1139/cjr41a-014

出版商:NRC Research Press    

年代:1941

数据来源: NRC