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 α = 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 ∈ ℕ) citation distribution is studied and shown to be the same as the first-citation distribution, for every n ∈ ℕ.