Magazine audience accumulation: basic modeling issues

This paper addresses two basic areas where mathematical models may be employed in the context of magazine audience accumulation. Specifically it will address the following modeling issues:
I. The development of a mathematical model to characterize the time based accumulation of the audience of a single issue of a publication
II. The development of a mathematical model to characterize the time based accumulation of audience for a sequence of issues of a publication.
The recognition that mathematical models were a necessary tool in magazine audience accumulation studies can be traced to some of the earliest US Magazine Audience studies. In the 1960 study of “Advertising Exposure by Weeks� conducted by Alfred Politz Research on behalf of Reader’s Digest, we find the following statement: “ The week-by-week estimates of cumulated issue exposures as derived from the survey showed in all cases a consistent growth pattern. However, to smooth the random variations in these estimates and hence to improve their reliability, it was decided to fit a curve of known characteristics to these data.�

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