Lotka's Law Research Articles

A characterization of the law of Lotka in terms of sampling

In order to model the variable T (the age of citations received by scientific works) with data elaborated by the Institute of Scientific Information, we have used some of the instruments already developed in the survival models to this type of retrospective analyses in the presence of censored data. This analysis is used because, usually, the citations of ages greater than or equal to 10 years appear added together. For a set of journals related to the field of Applied Economics, we have explored which models fit better among those commonly used. Two different approaches to assess the goodness-of-fit for each selected model have been suggested: an analysis through graphical methods and a formal analysis to estimate the parameters of each model by the method of maximum likelihood estimation with data censored to the right.

Emerald authorship data, Lotka's law and research productivity

Purpose – This paper offers a practical insight into the application of Lotka's law of author productivity to the question of how likely it is that an author will return to a particular publisher (rather than make another contribution to a subject literature, which is its usual application). The question of author loyalty, especially repeat visits, is one which is of great interest to publishers.

Internet usage transaction log studies: The next generation

Internet usage transaction log studies: The next generation

Fitting Lotka's law: Some cautionary observations on a recent paper by Newby et al. (2003)

Fitting Lotka's law: Some cautionary observations on a recent paper by Newby et al. (2003)

Solution of a problem of Buckland on the influence of obsolescence on scattering

In an old paper [M.K. Buckland. Are obsolescence and scattering related? Journal of Documentation 28 (3) (1972) 242–246] Buckland poses the question if certain types of obsolescence of scientific literature (in terms of age of citations) implies certain types of journal scattering (in terms of cited journals). This problem is reformulated in terms of one- and two-dimensional obsolescence and linked with one- and two-dimensional growth, the latter being studied by Naranan. Naranan shows that two-dimensional exponential growth (i.e. of the journals and of the articles in journals) implies Lotka's law, a law belonging to two-dimensional informetrics and describing scattering of literature in a concise way. In this way we obtain that exponential aging of journal citations and of article citations imply Lotka's law and a relation is given between the exponent α in Lotka's law and the aging rates of the two obsolescence processes studied.

Bibliometric analysis of biomedical publications on SSRI during 1980-2000.

We performed a bibliometric study of the scientific publications referring to selective serotonin reuptake inhibitors (SSRIs). The database used was EMBASE: Psychiatry. We applied the principal bibliometric indicators: Price's and Bradford's laws on the increase or dispersion of scientific literature, Lotka's law on the productivity of authors, the participation index (PaI) of countries, the productivity index (PI) of authors, and the collaboration index. By means of manual coding, documents were classified according to type of study and to the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV) or nonpsychiatric categories. We analysed 3,622 original documents published between 1980 and 2000. Our results show nonfulfilment of Price's law because production on SSRIs does not grow exponentially (r=0.937 vs. r = 0.946, after linear adjustment). The journal most employed is the Journal of Clinical Psychiatry (Bradford's first zone). The United States is the most productive country (PaI=41.50). The documents were distributed in four groups: experimental pharmacology (8.38%), tolerance and safety (34.94%), clinical efficacy (49.11%), and not specified (7.56%). The drug most studied was fluoxetine (1,745 articles), followed by paroxetine (659). The DSM-IV diagnostic categories most studied were depression (834), obsessive-compulsive disorder (171), and panic disorder (75). The control antidepressants most used in comparative clinical studies were amitriptyline (51) and imipramine (42). The results of the present study show that the SSRIs are not solely antidepressant drugs, but also have a wide range of uses both within the psychiatric sphere (especially in the field of anxiety) and outside it, which explains the considerable scientific production generated in relation to these drugs.

Open source software development and Lotka's Law: Bibliometric patterns in programming

AbstractThis research applies Lotka's Law to metadata on open source software development. Lotka's Law predicts the proportion of authors at different levels of productivity. Open source software development harnesses the creativity of thousands of programmers worldwide, is important to the progress of the Internet and many other computing environments, and yet has not been widely researched. We examine metadata from the Linux Software Map (LSM), which documents many open source projects, and Sourceforge, one of the largest resources for open source developers. Authoring patterns found are comparable to prior studies of Lotka's Law for scientific and scholarly publishing. Lotka's Law was found to be effective in understanding software development productivity patterns, and offer promise in predicting aggregate behavior of open source developers.

A Lei de Lotka na bibliometria brasileira

Usando os dados reportados em artigos publicados em revistas brasileiras e trabalhos apresentados em congressos nacionais, replicaram-se as aplicações da Lei de Lotka à literatura brasileira em 10 campos diferentes. Utilizou-se o modelo do poder inverso pelos métodos do mínimo quadrado e probabilidade máxima. Das 10 literaturas nacionais analisadas, somente a literatura de medicina, siderurgia, jaca e biblioteconomia ajustaram-se ao modelo do poder inverso generalizado pelo método dos mínimos quadrados. No entanto, só duas literaturas (veterinária e cartas do Arquivo Privado de Getúlio Vargas) não se ajustaram ao modelo quando se usou o método da máxima probabilidade. Para ambas literaturas, tentaram-se modelos diferentes. A literatura de veterinária ajustou-se à distribuição binomial negativa, e as cartas do Arquivo Privado de Getúlio Vargas ajustaram-se melhor à distribuição Gauss-Poisson Inversa Generalizada.

Duality revisited: Construction of fractional frequency distributions based on two dual Lotka laws

Fractional frequency distributions of, for example, authors with a certain (fractional) number of papers are very irregular and, therefore, not easy to model or to explain. This article gives a first attempt to this by assuming two simple Lotka laws (with exponent 2): one for the number of authors with n papers (total count here) and one for the number of papers with n authors, n ∈ N. Based on an earlier made convolution model of Egghe, interpreted and reworked now for discrete scores, we are able to produce theoretical fractional frequency distributions with only one parameter, which are in very close agreement with the practical ones as found in a large dataset produced earlier by Rao. The article also shows that (irregular) fractional frequency distributions are a consequence of Lotka's law, and are not examples of breakdowns of this famous historical law.

A new model that generates Lotka's law

AbstractIn this paper, we develop a new model for a process that generates Lotka's Law. We show that four relatively mild assumptions create a process that fits five different informetric distributions: rate of production, career duration, randomness, and Poisson distribution over time, as well as Lotka's Law. By simulation, we obtain good fits to three empirical samples that exhibit the extreme range of the observed parameters. The overall error is 7% or less. An advantage of this model is that the parameters can be linked to observable human factors. That is, the model is not merely descriptive, but also provides insight into the causes of differences between samples. Furthermore, the differences can be tested with powerful statistical tools.

Author inflation leads to a breakdown of Lotka's law

It is empirically shown that, even using the normal or total counting procedure, Lotka's law breaks down when articles with a large, i.e., more than hundred, number of authors are included in the bibliography. The explanation of this phenomenon is that the conditions for an application of the basic success-breeds-success model are not fulfilled any more. Studying articles with many authors means dealing with items (the articles) having multiple sources (the authors), hence Egghe's generalized success-breeds-success model, leading to not necessarily decreasing distributions, explains the observed irregularities.

Author inflation leads to a breakdown of Lotka's law

AbstractIt is empirically shown that, even using the normal or total counting procedure, Lotka's law breaks down when articles with a large, i.e., more than hundred, number of authors are included in the bibliography. The explanation of this phenomenon is that the conditions for an application of the basic success‐breeds‐success model are not fulfilled any more. Studying articles with many authors means dealing with items (the articles) having multiple sources (the authors), hence Egghe's generalized success‐breeds‐success model, leading to not necessarily decreasing distributions, explains the observed irregularities.

Power laws of research output. Evidence for journals of economics

In this paper we examine the validity of Lotka's law and Zipf'slaw for research output in 15 top journals of economics in the period 1977to 1997. Our data for individual authors satisfy a general form of Lotka'slaw. We find increasing competition over time among economists on the individuallevel. However, publications in top journals are concentrated heavily whenthe institutional level is under consideration. Research output of institutionscan be fit adequately by Zipf's law.

Scientific production: A statistical analysis of authors in physics, 1800-1900

We show that scientific production can be described by two variables: rate of production (rateof publications) and career duration. For 19th century physicists, we show that the time pattern ofproduction is random and Poisson distributed, contrary to the theory of cumulative advantage. Weshow that the exponential distribution provides excellent goodness-of-fit to rate of production andcareer duration. The good fits to these distributions can be explained naturally from the statisticsof exceedances. Thus, more powerful statistical tests and a better theoretical foundation isobtained for rate of production and career duration than has been the case for Lotka's Law.

Scientific production: A statistical analysis of authors in mathematical logic

We show that scientific production can be described by two variables: rate of production (rate of publications) and career duration. For mathematical logicians, we show that the time pattern of production is random and Poisson distributed, contrary to the theory of cumulative advantage. We show that the exponential distribution provides excellent goodness-of-fit to rate of production and a reasonable fit to career duration. The good fits to these distributions can be explained naturally from the statistics of exceedances. Thus, more powerful statistical tests and a better theoretical foundation is obtained for rate of production and career duration than has been the case for Lotka's Law.

Rescher's Principle of Decreasing Marginal Returns of Scientific Research

In his book "Scientific Progress", Rescher (1978, German ed. 1982, French ed. 1993)developed a principle of decreasing marginal returns of scientific research, which is based, interalia, on a law of logarithmic returns and on Lotka's law in a certain interpretation. In the presentpaper, the historical precursors and the meaning of the principle are sketched out. It is reported onsome empirical case studies concerning the principle spread over the literature. New bibliometricdata are used about 19th-century mathematics and physics. They confirm Rescher's principleapart from the early phases of the disciplines, where a square root law seems to be moreapplicable. The implication of the principle that the returns of different quality levels grow theslower, the higher the level, is valid. However, the time-derivative ratio between (logarithmized)investment in terms of manpower and returns in terms of first-rate contributors seems not to belinear, but rather to fluctuate vividly, pointing to the cyclical nature of scientific progress. Withregard to Rescher's principle, in the light of bibliometric indicators no difference occurs betweena natural science like physics and a formal science like mathematics. From mathematical progressof the 19th century, constant or increasing returns in the form of new formulas, theorems andaxioms are observed, which leads to a complementary interpretation of the principle of decreasingmarginal returns as a principle of scientific "mass production".

A Monte Carlo simulation model for studying evolution in age‐structured populations

This model provides for any number of genotypes defined by age-specific survival and fecundity rates in a population with completely overlapping generations and growing under the control of density-governing functions affecting survival or fecundity. It is tested in situations involving two alleles at one locus. Nonselection populations at Hardy–Weinberg equilibrium obey the ecogenetic law; i.e., each genotype follows Lotka's law regarding rate of increase and stable age distribution as if it were an independent true-breeding population. Populations experiencing age- and density-independent selection approximate this situation, and the changes in gene frequency are predicted by relative fitnesses bases on λ, the finite rate of increase of the genotypes. Polymorphic gene equilibria occurring at steady-state population sizes are determined by fitnesses based on R, the net reproductive rate. In examples involving differences in generation time produced by age-dependent differences in fecundity, the allele associated with longer generation time may be favored or opposed by selection, depending on whether the density-governing factor controlling population size affects survival or fecundity. If such genotypes have similar R's, a genetic equilibrium may be established if the population is governed by a density function acting upon fecundity.

Lotka's law and productivity index of authors in a scientific journal.

Lotka's law of scientific productivity is a bibliometric example: the number of authors against the number of contributions made by the authors was plotted on a logarithmic scale. The points were closely scattered around a straight line having a slope of -2. The purpose of this study was to apply information technology to real-world data and to quantify the extent of the bibliometric regularity that exists in the literature of dental science. We have analyzed the productivity index of authors (PI) in a scientific journal (Journal of American Dental Association). Details of a total of 4,088 papers published between 1966 and 1995 were extracted electronically from MEDLINE. The total number of authors was 5,589, responsible for 8,569 authorships. Only 0.8% of the authors presented a PI > = 1 (large producers), and 78.1% a PI = 0 (occasional authors). The number of authors publishing N papers was 1/N2.64 of those publishing one paper. The result suggested that repeated publications in the Journal were more difficult than those predicted by Lotka (1/N2).

A Bibliometric Study of Semiconductor Literature, 1978–1997

Semiconductor is the key element for information industry. The present study investigated the growth of semiconductor literature based on the database of INSPEC. Well-established bibliometric techniques, such as Bradford-Zipf's plot and Lotka's law have been employed to further explore the characteristics of semiconductor literature. Quantitative results on the literature growth, form of publication, research treatment, publishing country and language, author productivity and affiliate are reported. Moreover, from the Bradford-Zipf's plot, 25 core journals in semiconductor were identified and analyzed.

Science in India: performance of Council of Scientific and Industrial Research laboratories based on the productivity profile of scientists

Lotka's approach was used to study the performance of different Council of Scientific and Industrial Research (CSIR) laboratories in physical, biological and engineering sciences based on the productivity profile of scientists. The productivity profile of each laboratory, in terms of frequency distribution of scientists and their contributions was generated using the CSIR Directory of Scientists. The profiles were normalised using Lotka's approach. The applicability of Lotka's inverse power law (general and square) and other statistical distributions to the productivity of CSIR scientists at the overall agency level, the group of laboratories level and the individual laboratory level, within each subject was examined. Scientists contributing ten or less papers give a flat productivity distribution; between 11 and 29 papers, tend towards an inverse-square relationship; and more than 29 papers, indicate a flat productivity distribution. A geometric distribution best describes the distribution of scientists at all three levels.