λ -index: A new indicator based on generalized law in Information Production Processes

Despite the presence of skewness (i) that induces the possibility of existence of famous 80/20 law or others (like 90/10, 70/30, etc.), and (ii) that contributes to the relevance of indicators like h -type indicators, the law-indicator compliance in IPPs remained almost unexplored until recently. A recent exploration on the ability of the major existing basic h -type indicators to reflect the 80/20 rule found h -index as the best in that regard. Though considering 20 % of T (total sources/publications) or 0.2 T as an indicator, provided a slightly better alternative, the need for a better indicator was also reported. In this work, we devise such an indicator, namely the λ -index, by using a generalized law viz. ( 1 − ρ ) / ρ law wherein 80/20, 90/10, 70/30, etc., are special cases. The λ-index corresponds to the largest fraction of sources, ρ=λ/T, that have produced approximately (1−ρ) of all items. Interesting informetric properties of λ , including its linear dependence on T (total publications) that makes it remarkable and unique, are proven and discussed in comparison with other major base indicators. λ -index is found to exhibit indicator-law compliance for 80/20 law better than all the basic h -type indicators and 0.2 T indicator in multiple datasets. Possibilities for deciding the governing specific law (like 70/30 or 80/20) in a field using ρ is also discussed. Upon sensitivity analysis on profile of an author with redistribution of citations (to simulate a law change), λ is found to be better than other indicators in maintaining law-indicator compliance, hinting its importance to be used even in profiles having high volatility.