[4] Küster, E. Die Gallen der Pflanzen, Leipzig. 1911.
[5] Cook, Mel T. “Galls and Insects Producing Them.” Ohio Nat. 4:140-141. 1904.
THE GEOMETRY OF THE
TRANSLATED NORMAL CURVE.
Carl J. West, Ph. D.
Introduction. In curve tracing the graphic representation is constructed from the equation. Due largely to the requirements of statistics the converse, namely, to find the equation of the curve when the distribution of points is given, has become of interest. This problem is very different from the exercises of analytical geometry in which a given law of distribution of points is to be translated into algebraic language. For the presence in the statistical data of accidental irregularities makes it undesirable as well as practically impossible to obtain a curve passing through the points. Instead, a curve is “fitted” to the points, that is, a curve is passed among the points in accordance with some generally accepted principal such as that of least squares or the agreement of moments.
Aside from the straight line and the parabolas, the curves proposed by Pearson[6] have found acceptance. In order to derive curves which can be fitted to widely varying distributions of points, Professor F. Y. Edgeworth[7] has proposed to modify, to translate, the normal probability curve with unit standard deviation.
In this article we shall discuss the geometry of the curves which Edgeworth obtains by this transformation and derive a method for an approximate solution of the two equations, one of the fourth and the other of the sixth degree, which arise in the fitting of a curve of this class.