The source-item coverage of the exponential function

Abstract

Statistical distributions in the production of information are most often studied in the framework of Lotkaian informetrics. In this article, we recall some results of basic theory of Lotkaian informetrics, then we transpose methods (Theorem1) applied to Lotkaian distributions by Leo Egghe (Theorem 2) to the exponential distributions (Theorem 3, Theorem 4). We give examples and compare the results (Theorem 5). Finally, we propose to widen the problem using the concept of exponential informetric process (Theorem 6).

The source-effort coverage of an exponential informetric process

“…This inequality implies that if the mathematical power adjustment of an EIP is verified, then the same applies for a mathematical exponential adjustment. This result concurs with the mathematical adjustment of an IPP (see theorem 5 (Lafouge, 2007)). If N is infinite, it is worth making a parallel between the coefficient α of the exponential (41) and of the inverse power (49).…”

“…We can review the obtained results by distinguishing one case -where N, the maximum item per source density, is infinite -from the more realistic case that interests us -where N is finite, for both distributions (1) and (2). (i) Exponential Distributions (Lafouge, 2007) (a) N is infinite The adjustment conditions (3) are met by (2) if and only if:…”

“…An EIP (see section 3), (Lafouge and Prime--Claverie, 2005) is the broader version of an IPP (see section 2), commonly used to represent informetric processes. This article is composed of 4 parts and a conclusion: -- We review Egghe's results (Egghe, 2004) and their applications to exponential distributions (Lafouge, 2007) (see section 2). --Certain aspects linked to EIPs, such as the amount of effort, are detailed (see section 3).…”

On a formula for the h-index

“…1) The power-law/Pareto citation distribution, also known as 'inverse' power-law (Burrell, 2008), or Lotkaian informetric distribution or Lotka's law (Rousseau & Rousseau, 2000;Egghe, 2005a;Egghe & Rousseau, 2006;Lafouge, 2007), is probably the distribution most known and used in Informetrics. According to this probability model, the citation distribution function (or sizefrequency function) is equal to up to a normalizing factor, namely…”

On the relation between the Maximum Entropy Principle and the principle of Least Effort: The continuous case

“…-linear effort functions f(x) = x, in other words exponential distributions (Lafouge, 2007), in this case σ(f) = 0.…”