Comparison of different mathematical functions for the analysis of citation distribution of papers of individual authors

The citation distribution of papers of selected individual authors was analyzed using five mathematical functions: power-law, stretched exponential, logarithmic, binomial and Langmuir-type. The former two functions have previously been proposed in the literature whereas the remaining three are novel and are derived following the concepts of growth kinetics of crystals in the presence of additives which act as inhibitors of growth. Analysis of the data of citation distribution of papers of the authors revealed that the value of the goodness-of-the-fit parameter R2 was the highest for the empirical binomial relation, it was high and comparable for stretched exponential and Langmuir-type functions, relatively low for power law but it was the lowest for the logarithmic function. In the Langmuir-type function a parameter K, defined as Langmuir constant, characterizing the citation behavior of the authors has been identified. Based on the Langmuir-type function an expression for cumulative citations L relating the extrapolated value of citations l0 corresponding to rank n = 0 for an author and his/her constant K and the number N of paper receiving citation l ≥ 1 is also proposed.

► Citation rank-order distribution of selected authors is analyzed.
► Power-law, exponential, logarithmic, binomial and Langmuir-type relations are used.
► Among the functions, logarithmic, binomial and Langmuir-type functions are novel.
► Binomial, exponential and Langmuir-type functions describe the data satisfactorily.
► Parameter K of Langmuir-type function characterizes citation behavior of an author.