Price index and its relation to the mean and median reference age.

Abstract

This article consists of two parts. In the first part, we assume the simple decreasing exponential model for aging. In this case, we prove that the Price Index (the fraction of the references that are not older than a certain age) is a function of the mean reference age and also a function of the median reference age. Both functions are convexly decreasing, are 1 in 0 and tend to zero for the argument tending to infinity. In the second part, the more realistic lognormal aging model is used. We now show that the Price Index is not a pure function of the mean or median reference age, but a well-defined relation in the form of a typical cloud of points. This cloud (as, e.g., discussed in a 1995 article of W. Glänzel & U. Schoepflin) is explained using results from probability theory and statistics. New data (about reference ages in Journal of the American Society for Information Science) are produced that confirm the theoretical findings.