Investigating the universal distributions of normalized indicators and developing field-independent index

Using the dataset based on Thomson Reuters Scientific “Web of Science” the distributions of some well-known indicators, such as h-index and g-index, were investigated, and different citation behaviors across different scientific fields resulting from their field dependences were found. To develop a field-independent index, two scaling methods, based on average citation of subject category and journal, were used to normalize the citation received by each paper of a certain author. The distributions of the generalized h-indices in different fields were found to follow a lognormal function with mean and standard deviation of approximately −0.8 and 0.8, respectively. A field-independent index fi-index was then proposed, and its distribution was found to satisfy a universal power-law function with scaling exponent α approaching 3.0. Both the power-law and the lognormal universality of the distributions verified the field independence of these indicators. However, deciding which of the scaling methods is the better one is necessary for the validation of the field-independent index.