Biometrika Volume 1

Biometrika Volume 1

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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. 1902 edition. Excerpt: ...or in other cases the centroid vertical. Returning to equations (v) we see that the solution (vi) is even more approximate than might at first sight be imagined. For if we render identical the first n--1 moments of the two curves, the higher momenta of the curves become ipso facto more and more nearly identical the larger n may be. But such a term as vanishes if the higher moments are equal; for we may write n-11+1 i=W + ll, /, n+1(0)+," and accordingly d(0) 1 _ + etc. Thus if A=A', we have the factors (n -fin'), (/ +, -/i'n+1), (nn+i-Pn+t), etc. (&n(0) n+' (0) Thus besides the smallness of the factors, --., --V, ...etc., depending on n - + 1 r the hypothesis of convergeiicy in Maclaurin's expansion, we have the smallness of the factors fia--fin', /' +, ... depending on the fact that if n--1 moments of a curve are equal, the succeeding ones will be nearly equal. We conclude accordingly that equality of moments gives a good method of fitting curves to observations. It is this method of moments which I venture to suggest as a good systematic process, preferable to those in ordinary use when the method of least squares is too laborious or impracticable, for determining the constants of empirical or theoretical curves from observation. This is really the method which has been long in constant use for fitting the normal curve of errors y = yfili' to observations; it has been largely adopted by myself in fitting skew frequency curves to observations; and it becomes identical with that of least squares when we fit parabolic curves of any order to observations. It is then no approximation, but the accurate solution, for the expansion by Maclaurin's Theorem is finite. One great advantage of the method, as will more

Product details

  • Paperback | 142 pages
  • 189 x 246 x 8mm | 268g
  • United States
  • English
  • black & white illustrations
  • 123659522X
  • 9781236595225