98 BELL SYSTEM TECHNICAL JOURNAL 



the location and height of the peaks normally determined, the process 

 of constructing preliminary curves for the various intervals of the 

 detail series is, in many cases, considerably simplified. These pre- 

 liminary curves are then cross-sectioned and smoothed into a consistent 

 family. 



Finally the smooth curves of the cumulative and detail series are 

 checked with each other and averages are computed from these curves 

 as a check against the assumed average. When the minor discrep- 

 ancies disclosed by these checks have been corrected, normal curves 

 are plotted and comparisons are made with the actual distributions. 

 Further adjustments may then be necessary. 



Additional Factors in Deriving Normal 

 Distribution Curves 



The smoothing processes described above give a series of normal 8 

 distribution curves taking into account completely the effect of the 

 amount of the average upon the distribution. In some cases, how- 

 ever, it will be found that some outside factor has also a decided 

 effect upon the distribution. 



When the effect of an outside factor is apparent it may be neces- 

 sary to derive a series of normal distribution curves, each curve cor- 

 responding to a constant value of the factor under consideration. 

 If this is done, the curves are smoothed by cross-sectioning and the 

 various other methods described above so as to form a consistent and 

 reasonable family. The type of the final family derived will, how- 

 ever, depend largely upon the character of the relationships developed 

 during the smoothing process. For instance, in the case of main 

 station message rate service, a series of distribution curves was plotted, 

 one for each message allowance. In the course of smoothing these 

 curves it seemed reasonable that there might be a relationship between 

 the type of distribution and the proportional relationship of average 

 message use to message allowance. That is, with an annual message 

 allowance of 600 and an average annual message use of 400 the dis- 

 tribution of subscribers by amount of message use might be similar, 

 on a proportional basis, to the distribution of subscribers under an 

 annual message allowance of 900 with an average annual message 

 use of 600; or under an annual message allowance of 1,200 with an 

 average annual message use of 800. This idea was tested by use of 

 the various sets of normals which had been derived for the different 

 message allowances and was found to hold so closely that this pro- 



« See Note 6. 



