A simple model for citation curve

TL;DR

This paper introduces a simple, parameterized model for citation distributions that enables analytical derivation of citation indices and analysis of factors affecting author impact metrics.

Contribution

It presents a new, tractable mathematical equation for modeling citation curves, facilitating analysis and design of citation indices.

Findings

Derived closed-form expressions for citation indices

Analyzed the impact of time on citation metrics

Identified individual contributions to the Hirsch index

Abstract

There is considerable interest in the citation count for an author's publications. This has led to many proposals for citation indices for characterizing citation distributions. However, there is so far no tractable model to facilitate the analysis of these distributions and the design of these indices. This paper presents a simple equation for such design and analysis. The equation has three parameters that are calibrated by three geometrical characteristics of a citation distribution. Its simple form makes it tractable. To demonstrate, the equation is used to derive closed-form expressions for various citation indices, analyze the effect of time and identify individual contribution to the Hirsch index for a group.