An Essay On The Numerical Verification And Informetric Analysis Of The Shifted Power Function

The accumulation of quantitative data marks the beginning of science while inducing mathematical representations from massive data is the only way leading to the formation of science.The bibliometrics,the scientometrics and the informetrics,born in the field of library and information science,are guiding the latter to developing from experienced skills to scientific studies.The source and the item,the unified representation of metrology study objects,are usually skewly distributed which lights the inherent advantages of power function models to probing into relation between informational entities.Among them,the shifted power function(SPF)particularly stands out.This paper attempts to conduct a full range research on SPF,from the model itself to its logical extension as well as from the theory core to its practical use.To reveal the mathematical mechanism and theoretical value of SPF,general informetric distribution is explored with using fully-distributed data of subjects and journals.Comparing with shifted power function with exponential cutoff(PFE)and decreasing exponential function(DEF),the SPF expresses a better balance of data fitting and theoretical analysis,and can be used as a core function.The PFE,which is logic extension of SPF,shows the best fitting with large samples,but loses mathematical analytics,while the DEF does the exact opposites.To expand the logical denotation of SPF,three typical functions,namely the decreasing exponential function,the Weibull function and the half-logistic function,are selected and the mutual transformation between different functions is formulated from the perspective of mathematics.Based on these transfer relations,interconnected model is established and can be used to explain the traditional two-variable scenario as well as the new three-variable scenario.The establishment of interconnected model enables SPF to cross the border of metrology and thus support the exchange and integration of knowledge from multidisciplines.To explore the practical use of SPF,we focus on the topic of academic evaluation.A theoretical model is set up to estimate the ratio of e-index and h-index(e/h)in publication-citation distribution with DEF as a comparison.Using data covering subject,journal,country and institution levels,it is revealed that SPF overestimates e/h while DEF underestimates e/h.With deep analysis,it is found that apart from system error,neither SPF nor DEF could tolerate the extreme randomness of sample points in h-core for their low complexity which is the direct answer to estimation error while the false assumption of model parameters causes samples'theoretical distribution deviate from its real distribution which is the essential explanation for estimation error.Considering h-core's small proportion in the entire publication-citation distribution and SPF or DEF's good property for theoretical analysis together,it is believed that the ratio model of e-index and h-index can be used as general theoretical references.Mathematical models occur as the infrastructure work of informetric distribution research,while SPF or SPF-related models may provide a feasible approach to study source-item relation and to unify all informetric distributions.The research by this paper is expected to constitute a systematic framework of SPF in the feature and develop the existing Lotkaian informetrics,beginning with which as a foothold,we can better understand source-item relation or more generalized association between informational entities and draw the realization from quantitative description to relationship representation.