DeForest's formula for 'an unsymmetrical probability curve' / Shinkishi Hatai.

  • Hatai, Shinkishi.
Date:
1910
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Licence: In copyright

Credit: DeForest's formula for 'an unsymmetrical probability curve' / Shinkishi Hatai. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

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    Reprinted from the Anatomical Record, Vol. 4, No. V \ ? ' M V ■ ->*•**- DeFOREST’S formula for “an unsymmetrical PROBABILITY CURVE” In presenting a long-forgotten investigation by E. L. DeFor- est (’82-’83) on “an unsymmetrical probability curve,” the writer wishes to call attention to the fact that the first systematic analy- sis of the subject was attempted by DeForest and as a result he obtained a formula which is identical with that for Professor Pearson’s (’95) generalized probability curve. DeForest suggests further that by retaining the higher derivatives a more general formula, of which the formula already found will be a particular case, may be obtained from his original differential equation. Thus DeForest’s investigation is not only interesting from an historical standpoint, but still more from the fact that the same formula, though in different terms, has been derived from entirely different methods of analysis by Professor Pearson. This fact furnishes good evidence as to the validity of Professor Pearson’s theoretical assumption. As the investigation was published a number of years ago, the original paper by DeForest is difficult to obtain, and so, for the reader who is anxious to see the method of mathematical analysis adopted by him, I venture to present in the following pages some of the important points which directly concern the derivation of his final formula. I shall also add a mathematical process of transformation of Professor Pearson’s formula to that of DeForest. For numerous other important and interesting points, the reader must refer to the original memoirs. DeForest employed this reasoning: Let the following be a given polynomial X— m Z~m + + X_1 Z~l + Xo + Xj Zl + + \mZm. (1) SHINKISHI HATAI The Wistar Institute of Anatomy THE ANATOMICAL RECORD, VOL. 4, NO. 8.