Die Theorie der Collectivgegenstände.
159
und
Px — Po ' cos-"V> • cxp[— vxfj \ x — a tang #,	(32)
wo je nach dem Wertlie gewisser Constanten die eine oder die andere Function in Kraft tritt. Zur Rechtfertigung sagt er: >Until we know very much more definitely, than we do at present, how the size of an organ in any individual, say, depends on the sizes of the same organ in its ancestors, ore what are the nature of the causes which lead to the determination of prices, or of income, Or of mortality at a given age, I do not see that we have any right to select as our sole frequency curve the normal type
y = y0 • c~px*
in preference to the far more general
y = Vo
which not only includes the former, but supplies the element of skewness which is undoubtedly present in many statistical frequency distributions. As we may look upon the former as a limit to a cointossing series, so the latter represents a limit to teetotum-spinning and card-drawing experiments. It is not easy to realise why nature or economics should, from the standpoint of chance, be more akin to tossing than to teetotum-spinning or card-dealing. At any rate, from purely utilitarian and prudent motives, we are justified so long as the analysis is manageable, in using the more general form. It will always give us a measure of the divergence of particular statistics from the normal type, and in many cases of skew frequency, it can be used when it would be the height of absurdity to apply the normal curve at all. «
Der kritische Werth, von dem die Anwendbarkeit des einen oder anderen Curventypus abhängt, ist in der Schreibweise Pearson’s:
2«,(3p’ — hJ + 3uj,	(33)
wo Vu f<3, ,«4 die sogenannten Momente der Vertheilungstafel oder Häufigkeitscurve bezüglich des arithmetischen Mittels sind. Diese