Fairness in the three-dimensional model for citation impact

We analyse the usefulness of Jain’s fairness measure and the related Prathap’s bibliometric z-index as proxies when estimating the parameters of the 3DSI (three dimensions of scientific impact) model

Interpretable reparameterisations of citation models

This paper aims to find the reasons why some citation models can predict a set of specific bibliometric indices extremely well. We show why fitting a model that preserves the total sum of a vector can be beneficial in the case of heavy-tailed data that are frequently observed in informetrics and similar disciplines. Based on this observation, we introduce the reparameterised versions of the discrete generalised beta distribution (DGBD) and power law models that preserve the total sum of elements in a citation vector and, as a byproduct, they enjoy much better predictive power when predicting many bibliometric indices as well as partial cumulative sums. This also results in the underlying model parameters' being easier to fit numerically. Moreover, they are also more interpretable. Namely, just like in our recently-introduced 3DSI (three dimensions of scientific impact) model, we have a clear distinction between the coefficients determining the total productivity (size), total impact (sum), and those that affect the shape of the resulting theoretical curve

Time to vote: Temporal clustering of user activity on Stack Overflow

Question-and-answer (Q&A) sites improve access to information and ease transfer of knowledge. In recent years, they have grown in popularity and importance, enabling research on behavioral patterns of their users. We study the dynamics related to the casting of 7 M votes across a sample of 700 k posts on Stack Overflow, a large community of professional software developers. We employ log-Gaussian mixture modeling and Markov chains to formulate a simple yet elegant description of the considered phenomena. We indicate that the interevent times can naturally be clustered into 3 typical time scales: those which occur within hours, weeks, and months and show how the events become rarer and rarer as time passes. It turns out that the posts' popularity in a short period after publication is a weak predictor of its overall success, contrary to what was observed, for example, in case of YouTube clips. Nonetheless, the sleeping beauties sometimes awake and can receive bursts of votes following each other relatively quickly

Gini-stable Lorenz curves and their relation to the generalised Pareto distribution

We introduce an iterative discrete information production process where we can extend ordered normalised vectors by new elements based on a simple affine transformation, while preserving the predefined level of inequality, G, as measured by the Gini index. Then, we derive the family of empirical Lorenz curves of the corresponding vectors and prove that it is stochastically ordered with respect to both the sample size and G which plays the role of the uncertainty parameter. We prove that asymptotically, we obtain all, and only, Lorenz curves generated by a new, intuitive parametrisation of the finite-mean Pickands' Generalised Pareto Distribution (GPD) that unifies three other families, namely: the Pareto Type II, exponential, and scaled beta distributions. The family is not only totally ordered with respect to the parameter G, but also, thanks to our derivations, has a nice underlying interpretation. Our result may thus shed a new light on the genesis of this family of distributions. Our model fits bibliometric, informetric, socioeconomic, and environmental data reasonably well. It is quite user-friendly for it only depends on the sample size and its Gini index

Accidentality in journal citation patterns

We study an agent-based model for generating citation distributions in complex networks of scientific papers, where a fraction of citations is allotted according to the preferential attachment rule (rich get richer) and the remainder is allocated accidentally (purely at random, uniformly). Previously, we derived and analysed such a process in the context of describing individual authors, but now we apply it to scientific journals in computer and information sciences. Based on the large DBLP dataset as well as the CORE (Computing Research and Education Association of Australasia) journal ranking, we find that the impact of journals is correlated with the degree of accidentality of their citation distribution. Citations to impactful journals tend to be more preferential, while citations to lower-ranked journals are distributed in a more accidental manner. Further, applied fields of research such as artificial intelligence seem to be driven by a stronger preferential component - and hence have a higher degree of inequality - than the more theoretical ones, e.g., mathematics and computation theory

Power laws, the Price model, and the Pareto type-2 distribution

We consider a version of D. Price's model for the growth of a bibliographic network, where in each iteration, a constant number of citations is randomly allocated according to a weighted combination of the accidental (uniformly distributed) and the preferential (rich-get-richer) rule. Instead of relying on the typical master equation approach, we formulate and solve this problem in terms of the rank–size distribution. We show that, asymptotically, such a process leads to a Pareto-type 2 distribution with a new, appealingly interpretable parametrisation. We prove that the solution to the Price model expressed in terms of the rank–size distribution coincides with the expected values of order statistics in an independent Paretian sample. An empirical analysis of a large repository of academic papers yields a good fit not only in the tail of the distribution (as it is usually the case in the power law-like framework), but also across a significantly larger fraction of the data domain