Researches into the theory of probabiHty 



33 



Eighth Example. Distribution of glands of swine, given in Example I, treated 

 as belonging to type B of frequenci/ curves. 



As has beeu already remarked, the frequency curve in this case may alterna- 

 tively be regarded as belonging to type Ä or to type B. I have treated it before 

 as an ^-curve, and will now consider the same numbers belonging to a curve of 

 type B. 



Using the 4"' method above, we obtain, according to the formulas (25) and (29): 



b — c = 2.082 a, 



X = 4.326, 

 0) = 0.480 a, 



Y;, — 0.0i2, 



= — 0.16. 



Diagram 16 shows the comparison with the observations ^). As might be ex- 

 pected, the agreement is somewhat closer at the discontinuous end than in example I, 

 but, generally speaking, either curve may be used to represent the observations. 

 Theoretically the curve B may be preferred. 



Other examples of frequency curves belonging to type B may be gathered 

 from different domains of statistics. I will conhne myself, however, to the above 

 given examples till two desiderata of the theory oï these curves have been filled up. 

 In the first place it is necessary to calculate a table of the function '{>-^(.r), giving 

 the values of this function for fractional values of the argument. In the second 

 place it is necessary to calculate the error of the formula 



CO Ï (,/'co + cf F {.au + = ï y F {.<■), 



on which the computation of the parameters of the curve depends. 



VI. Dissection of a frequency curve into components. 



This problem has been first treated by Pearson. I have made during my 

 lectures on the theory of probability this year some researches into this subject, and 

 I will give here some extracts of the results obtained, reserving a fuller report till 

 another opportunity. 



Let us suppose that a given frequency curve is the resultant of two frequency 

 curves belonging to the type A, with the corresponding values of ß,, and equal 

 to zero. We hence have 



(34) i"(.'1 = q'fi + f,'f,, 



') In constructing the curve, tlie coefficients and -^^ have been neglected. 

 Lunds Univ:s Årsskrift. N. V. Aid. 2. Bd 1. 



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