Mathematical Contributions to the Theory of Evolution Volume 13-17

Mathematical Contributions to the Theory of Evolution Volume 13-17

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 edition. Excerpt: ...moments. For these reasons it seems idle to propose going beyond the 6th to 8th moments, or the 3rd to 5, b product-moments. Practical experience suggests that little is to be gained by using moments beyond the 6th, or product moments beyond the 3rt. A quartic regression curve may be useful occasionally, but it has yet to justify its necessity. As our object is not to reproduce the given data, but to provide a graduation for them, which smooths down the errors of random sampling, we believe that any legitimate and practical theory must discard the high moments and high product moments with which Thiele and Lipps propose to deal. (iv.) There is one point to which reference ought to be made. Some reader may enquire why the method of my paper on curving fitting should not be applied to these regression curves in general, as we have in practice once or twice already applied it. It would seem that that method is the easier, involving in the case of the quartic only quantities analogous to our r, e, and 6. The answer is "On the Systematic Fittings of Curves to Observations and Measurements." 'Biometrika, ' vol. I., pp. 265-303, and vol. II., pp. 1-23, especially the latter, pp. 11-15. straightforward: that process supposes every yTr to have equal weight, or nxf to be the same for each array. Hence the higher moments of the x-character, which are really involved, can be written down without calculation once and for all. The complexity of our present investigation arises from the introduction of the weighting into the calculation of the moments of the a;-character, as well as into that of the product moments r, e,, 6. Our results therefore, although they might not look so good on a graph of the regression curve, would be...
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Product details

  • Paperback | 50 pages
  • 189 x 246 x 3mm | 109g
  • United States
  • English
  • black & white illustrations
  • 1236930754
  • 9781236930750