(untitled) (Statistics, Optimization & Information Computing, 2025)
One of the most noticeable ways of illustrating the degree of concentration in a theoretical or empirical frequency distribution is via the Leimkuhler curve. Leimkuhler curve is particularly appropriate in the field of informetrics where the variable of interest is the number of citations, relevant references, borrowing of a monograph, etc. In informetrics, interest usually focuses on the most productive sources, and the equivalent graphical representation is via the Leimkuhler curve. In this paper, some statistical properties of the Leimkuhler curve, a plot of the cumulative proportions of total productivity against the cumulative proportions of sources, where the sources are ordered non-increasingly concerning their productivity levels are discussed. Also, some aspects of the Leimkuhler curve and its connection with other criteria are derived. Finally, several concentration measures are obtained using the data of the impact factors in eight scientific fields.