Two indicators rule them all: Mean and standard deviation used to calculate other journal indicators based on log-normal distribution of citation counts

Abstract

Two journal-level indicators, respectively the mean ($m^i$) and the standard deviation ($v^i$) are proposed to be the core indicators of each journal and we show that quite several other indicators can be calculated from those two core indicators, assuming that yearly citation counts of papers in each journal follows more or less a log-normal distribution. Those other journal-level indicators include journal h index, journal one-by-one-sample comparison citation success index $S_j^i$, journal multiple-sample $K^i-K^j$ comparison success rate $S_{j,K^j}^{i,K^i }$, and minimum representative sizes $\kappa_j^i$ and $\kappa_i^j$, the average ranking of all papers in a journal in a set of journals($R^t$). We find that those indicators are consistent with those calculated directly using the raw citation data ($C^i=\{c_1^i,c_2^i,\dots,c_{N^i}^i \},\forall i$) of journals. In addition to its theoretical significance, the ability to estimate other indicators from core indicators has practical implications. This feature enables individuals who lack access to raw citation count data to utilize other indicators by simply using core indicators, which are typically easily accessible.