## Download PDF by William Palin Elderton, Visit Amazon's Norman Lloyd Johnson: Systems of Frequency Curves

By William Palin Elderton, Visit Amazon's Norman Lloyd Johnson Page, search results, Learn about Author Central, Norman Lloyd Johnson,

ISBN-10: 0521073693

ISBN-13: 9780521073691

ISBN-10: 0521093368

ISBN-13: 9780521093361

Sir William Elderton's Frequency Curves and Correlation was once first released in 1906 and as a result 3 new versions have been released. It has lengthy loved acceptance as a resource of transparent descriptions of the sensible use of Pearson and in addition Gram-Charlie platforms of frequency curves. Professor Johnson has considerably revised this ebook. the fabric on correlations has been passed over; descriptions of additional sorts of frequency curves were further; the therapy of frequency surfaces has been recast and broadened; and the chance has been taken to amend the unique textual content within the mild of later learn. the purpose of this ebook continues to be basically sensible. there's no test at encyclopaedic assurance of all identified structures of frequency curves and surfaces. it's going to be of especial worth as a brief reference ebook (for statisticians and non-statisticians alike) for formulae and strategies utilized in becoming frequency curves.

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**Extra info for Systems of Frequency Curves**

**Sample text**

R = 5-186811 logr = 0-7149004 r+l = 6-186811 log ( r + l ) = 0-7914669 r+2 = 7-186811 log(r+2) = 0-8565363 r—2 = 3-186811 log(r—2) = 0-5033563 a±+a2 = 15-52366 ax = 1-99638 m1 = 0-409833 a2 = 13-52728 Mean—mode = 2-223116 m2 = 2-776978 It will be noted that the expression y^{j8 1 (r+2) 2 +16(r+l)} occurs in both the values of (04+0^) and m. The mean is at age 12+5-175 X 5 = 37-8750, and the mode at age 37-8750—2-223116x5 = 26-75942. The skewness is 0-8032. The calculation of log y0 is as follows: log N = 3-00000 colog(a 1 +a 2 ) = 2-80901 m1logm1 = 1-84123 m 2 l o g m 2 = 1-23179 colog(r-2)r-2 = 2-39590 log r(r) = 1-50406 colog r ( m !

94-95). Example As an example of this type the figures in Table 1 (Example 2) may be used. The moments were first found by the summation method (see Chapter 3, § 9) as shown in the following table. The reader can check the result by recalculating the moments by the more direct method, taking age 42 as the arbitrary origin. This is how I should myself usually do the work; I only use the summation method when the series is a very long one, and I give it here merely by way of example. Central group Exposed to risk Example 2 of Table 1 17 22 27 32 37 42 47 52 57 62 67 72 77 82 87 Totals age of First Second Third Fourth sum sum sum sum 34 145 156 145 123 103 86 71 55 37 21 13 7 3 1 1000 5 175 4 175 3 209 2 388 1 723 1203 19 809 14 634 10 459 7 250 4 862 3 139 1 936 1 130 64 389 44 580 29 946 19 487 12 237 7 375 4 236 2 300 1 170 1000 5175 966 821 665 520 397 294 208 137 82 45 24 11 4 1 S2 = #4 #5 806 512 304 167 85 40 16 5 1 19 809 5175/1000 = 19 809/1000 = 64 389/1000 = 186 638/1000 618 314 147 62 22 6 1 64 389 = 5-175 = 19-809 = 64-389 = 186-638 552 238 91 29 7 1 186 638 54 Calculation The next step is to find the moments about the centroid vertical using the formulae on page 51, and, in this case, as no adjustments * were made in the moments the i>'s and JLC'S are the same.

The semi-invariants (or half-invariants) used by Thiele and other writers can be obtained from moments. The second and third semi-invariants are the same as the second and third moments about the mean and the fourth semi-invariant is the fourth moment less three times the square of the second moment (/x4 — 3/i|). 22 Method of moments 12. * We shall now use this arrangement with the 'factorial moment' form. A little care is necessary, because, though there is no difficulty about the interpretation of the sums on the positive side of the selected point, the moments for the terms on the negative side assume that multiplications are made by the powers of negative quantities.

### Systems of Frequency Curves by William Palin Elderton, Visit Amazon's Norman Lloyd Johnson Page, search results, Learn about Author Central, Norman Lloyd Johnson,

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