Comparative study of scaling parameters and research output of selected highly- and moderately-cited individual authors

The real data of cumulative citations l_n of selected nth paper of individual N papers published by some highly- and moderately-cited individual authors are analyzed to compare Hirsch and Hirsch-type indices h, h₁, h_f and h_m, and citation radii R and R_f from consideration of: (1) the number A_n of coauthors of the paper, (2) the normalization of citations l_n and cumulative fraction l_nf of citation of the nth paper by mean and median citations of the citations l_n of all N_c cited papers, and (3) the determination of effective rank n_eff of the l_nf citations. Analysis of the l_n(n), l_nf(n) and l_nf(n_eff) data was also carried out by using a Langmuir-type function l = l₀[1-aKn/(1+Kn)], where l denotes the citations l_n and l_nf of all cited N_c papers arranged in the decreasing order, a is an effectiveness parameter, K is the so-called Langmuir constant, n denotes the rank n or n_eff of citations and l₀ is the value of l when n or n_eff approaches zero. For a comparison of the publication output of different authors it was found that the h_m index is more consistent than other indices, and it can be normalized to account for the publication career of different authors. However, Langmuir-type function is not adequate for comparison of the publication output of different authors because it describes the rank-order distribution patterns satisfactorily in terms of two parameters. To compare the publication output of different authors independent of their career length t, it is suggested to use scaling parameters h/t, h_f/t and h_m/t.