Citation age data and the obsolescence function - fits and explantations

Abstract

The paper deals with the shape of the obsolescence function, which one can construct, based on the age data of reference lists. This paper shows that the obsolescence factor (aging factor) a is not a constant but merely a function of time. This jeopardizes this factor as a useful measure. We show (by experiment and also mathematically) that the function a has a minimum, which is obtained at a time t later than the time at which the maximum of the number of citations is reached. We then fit sets of citation data by using the lognormal distribution (other distributions do not fit well). Analytical calculations with this function a are indeed valid for these data. These arguments also yield a description of the utility function u and the total utility U. The latter can be used in comparing the "total lives" of the literature in various subjects.