Lotka's law (Lotka 1926 ) states that the number of authors with n publications, where n = 1, 2, 3,.. can be described by an inverse power law of the form
where f ( n ) denotes the number of authors
computed the syntactic complexity of this language. Stepanov and Tsa ( 2008 ) proved that different lexical entries displayed different syntactic distribution.
The Lotka law states that in a certain period of time, f(x) , the percentage of the
The purpose of this article is to provide information about author productivity as reflected through the number of occurrences
of personal name headings in the Slovenian online catalogue COBIB. Only authors associated with monographs are treated. So,
author productivity of monographs that has not been widely researched is empirically examined to determine conformity or nonconformity
to Lotka’s law. A random sample of 1.600 Slovenian authors is drawn from the authority file CONOR. Next, the authors are searched
in COBIB and each attributed the number of monographs. Using the formula: xny = c, the values of the exponent n and the constant c are computed and the Kolmogorov-Smirnov test is applied. The paper shows that the author productivity distribution predicted
by Lotka also holds for the occurrences of personal name headings in COBIB.
In order to determine the Lotka parameters for a bibliography, one usually uses the complete data set. In this paper it is shown that it is possible to use only a fraction of the original data, namely by sampling randomly. However, sampling can be done either by source, i.e. selecting a fraction of the authors, or by item, i.e. selecting a fraction of the publications. It is shown here both by experiments, using computer simulations, and by mathematical approach, that only sampling by source is allowed for the mentioned purpose. Item samples give a completely disturbed idea about the Lotka law for the bibliography. From source sample size equal to 10% onwards, one gets good results. For the calculation of the Lotka exponent, a known, simple and fitting method is used and refined.
A linear correlation exists between the Lotka frequency and Zipf rank distribution functions. Relatively good correlation coefficients were found, but slope constants are not consistent with theory. They show that information distributions are not homogeneous and cannot be completely described by two parameter functions.
The following problem has never been studied : Given A, the total number of items (e.g. articles) and T, the total number
of sources (e.g. journals that contain these articles) (hence A>T), when is there a Lotka function.
The paper examines whether productivity differences among individual researchers are larger in some fields of learning than in others. Productivity patterns in the natural sciences, the medical sciences, the social sciences, and the humanities are compared by the use of unweighted and weighted publication counts. Irrespective of whether total number of publications or a refined indicator taking account of type of publication and multiple authorship are used, there are no essential differences in publishing inequality between the various fields. About 20% of the tenured faculty at Norwegian universities produce 50% of the total output, and the most prolific half of the researchers account for almost 85% of the output. The results are discussed in relation to Lotka's law.
The paper explores the possibility of using a new variable represented by the number of collaborators per author as a substitute
for the number of papers in Lotka's distribution to predict the productivity strata. On the basis of a case study in theoretical
population genetics it is concluded that the number of collaborators per author has not proved to be a good substitute in
the Lotka's distribution, which is in contrast to Qin's results.
A complex structure measure for social groups was applied to the structure of citations in a journal. The citation structure reflected LOTKA's law on the various levels of group structure measure. On the first structure level the reciprocal effect of social and cognitive factors became discernible. The different hierarchical levels of the structure measure were a reflection of the logarithm of number of publications per author obtained in a group of authors with a definite number of publications.
A bibliography of entomological research in Nigeria, 1900–1973 totally 1720 publications was analysed to study the author productivity patterns and to test the applicability of Lotka's law for the obtained distributions. Four different files were generated, one for the publications of all the authors, second for the publications by first authors, third for single authors and fourth for coauthors. Lotka's law in its original form as inverse square law does not apply to any of the four data sets. However, it does apply in its generalised form with the calculated values of characteristic exponent . The values of were found to be 1.9, 1.8, 2.2 and 2.4 for the four different data sets. K-S statistical test was aplied to test the applicability of generalised form of Lotka's law. The maximum difference in the observed and estimated values of the proportions of authors was found to be highly insignificant at 0.01 level of significance in each of the four cases.