Theory of first-citation distributions and applications

The general relation between the first-citation distribution and the general citation-age-distribution is shown. It is shown that, if Lotka's exponent alpha = 2, both distributions are the same. In light of the above results, and as a simple case, the exponential distribution and the lognormal distribution have been tested and accepted. Also. the n(th) (n is an element of N) citation distribution is studied and shown to be the same as the first-citation distribution, for every n is an element of N. (C) 2001 Elsevier Science Ltd. All rights reserved.