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BELL SYSTEM TECHNICAL JOURNAL 



The approximation is in this case well nigh perfect and comes 

 much closer to the true values of the point binomial than any of the 

 six approximations as given in Dr. Shewhart's article in the January 

 1924 number of this Journal. It also shows that with exactly the same 

 amount of computation as that involved in the so-called Charlier A 

 series, we can reach greatly improved results through the inclusion 

 of the sixth derivative in the series. This arises from the important 

 fact that once we have computed the coefficients Cs and Ci, it is not 

 necessary to calculate Ce since ce = ^Cs' approximately. Moreover, 

 since extensive tables, notably those of Jorgensen, now are available 

 for the normal function and its first six derivatives, there seems no 

 good reason why we should not use the more exact approximation than 

 the inexact formula by Bowley. 



In conclusion, it might be well to emphasize the fact that while it is 

 important to consider the relative order of magnitudes of the separate 

 terms in the Gram series when we use the methods of semi-invariants 

 or of moments, such restrictions are not necessary if we use the method 

 of least squares in conjunction with properly determined weights. 



Arne Fisher. 

 December 10, 1926. 



To the Editor of the Bell System Technical Journal: 



I have read Mr. Fisher's communication with considerable interest. 

 We who do not read the Scandinavian language owe much to him for 

 his very able amplification and interpretation of many important 

 contributions of the Scandinavian school of mathematical statisticians 

 and this debt has been increased by the above communication insofar 

 as it brings to light a very interesting relationship (the discovery of 



