This article consists of two parts. In the first part, we
In Gla ยจnzel and Schoepflin (1995), a graph of PI 2 assume the simple decreasing exponential model for (1100) versus the mean reference age is produced. With aging. In this case, we prove that the Price Index (the permission of the authors, and publisher, this graph is fraction of the references that are not older than a cerpresented again (Fig. 1).
tain age) is a function of the mean reference age and
This is a remarkable graph. First of all, the overall also a function of the median reference age. Both functions are convexly decreasing, are 1 in 0 and tend to zero tendency is convexly decreasing, although the relation is for the argument tending to infinity. not a pure function: Indeed, the middle part contains an
In the second part, the more realistic lognormal aging apparently thick cloud of points which seems to be strucmodel is used. We now show that the Price Index is not tural, and it smoothly disappears in the beginning and the a pure function of the mean or median reference age, end of the graph. Furthermore, it seems to be clear that but a well-defined relation in the form of a typical cloud of points. This cloud (as, e.g., discussed in a 1995 article PI 2 ร 1 for the mean reference age going to zero (the of W. Gla ยจnzel & U. Schoepflin) is explained using results graph says 100%, being a fraction 1) and that PI 2 goes from probability theory and statistics. New data (about to zero for the mean reference age going to infinity. How reference ages in Journal of the American Society for can this be explained? Information Science) are produced that confirm the the-A good scientific method consists of starting with oretical findings. * Permanent address.
of MA, but a mathematical relation (a cloud). The shape of this cloud is explained to be convexly decreasing (as