A proposal for a novel impact factor as an alternative to the JCR impact factor

One disadvantage of the JCR impact factor, the most commonly used assessment tool for ranking and evaluating scientific journals, is its inability in distinguishing among different shapes of citation distribution curves, leading to unfair evaluation of journals in some cases. This paper aims to put forward an alternative impact factor (IF′) that can properly reflect citation distributions. The two impact factors are linearly and positively correlated, and have roughly the same order of magnitude. Because of the ability of IF′ in distinguishing among different shapes of citation distribution curves, IF′ may properly reflect the academic performance of a scientific journal in a way that is different from the JCR impact factor with some unique features that reward journals with highly cited papers. Therefore, it is suggested that IF′ could be used to complement the JCR impact factor.


Results
Derivation of an alternative impact factor, IF9. To complement the h-index 6 , the e-index 18 and t-index 20 were proposed. The e-index is the square root of the excess citations over h 2 in the h-core. The tindex is the square root of the h-tail citations 19 . Therefore, the area under the citation distribution curve is divided by the h-index into three parts, representing the h 2 , the excess citations (e 2 ) and h-tail citations (t 2 ), respectively. To capture the main shape of the citation distribution curve, the head-tail ratio, denoted by r, was defined 21 The three cases of r . 1, r 5 1 and r , 1 correspond to three types of the citation distribution functions. The shapes of citation distribution functions for r . 1 are peaked, and for r , 1 the shapes of the citation functions are flat with a long tail, whereas for r 5 1 the citation functions are roughly symmetrical with respect to the diagonal line of the coordinate system. A number of authors attempted to apply the h-index to complement or correct the JCR impact factor [14][15][16] . It should be pointed out that we cannot simply use the h-index to complement or correct the JCR impact factor. This is due to the fact that the h-index by itself does not carry information for the excess and h-tail citations, which can play an even more dominant role than the h-index in determining the shape of citation distribution curve. As pointed out previously 21 , when r . 1, especially r ? 1, the h-index under-estimates the academic performance of a scientific journal,whereas when r , 1, especially r = 1, the h-index over-estimates the academic performance of a scientific journal. When r 5 1, the h-index properly reflects the academic performance of a scientific journal.
To provide an alternative evaluation of the academic performance of a scientific journal, we propose a novel impact factor, denoted by IF9, to complement the JCR impact factor, defined by where h9 is the h9-index 21 .
The citations received by all papers in the h-core, denoted by C h-core , are where cit j are the citations received by the j th paper. Letting e 2 denote the excess citations within the h-core, we find 18 where R is the R-index 22 . So, Meanwhile, the t-index was defined by 20 where C total is the number of total citations received by all papers published. Finally, we have and Correlation between IF9 and the JCR impact factor. Based on the data derived from the JCR and WoS, the related parameters including the total citations C total , the h-index, e-index, t-index, the head-tail ration r and IF9 are calculated for each of the 227 journals in the category of biochemistry and molecular biology. To save printing space, only the front ten journals in the alphabetic order are listed in Table 1. The related data for all the 227 journals are listed in the Appendix-1. As we can see from Table 1 that the head-tail ratio r for nine of the ten journals listed is all less than 1. Indeed, for almost all of the 227 journals listed in the Appendix-1, the values of r are less than 1. To study the relation between the two impact factors, the correlation between IF9 and the JCR impact factor is shown in Fig. 1. It is seen that IF9 is highly linearly and positively correlated with the JCR impact factor, as reflected by the fact that the correlation coefficient is as high as 0.89. Of note, IF9 and the JCR impact factor have roughly the same order of magnitude. The above two features make IF9 relatively easy to be accepted by the academic community. Applications of IF9. As an application, we show here the rankings of the 227 journals in the category of biochemistry and molecular biology based on IF9. For comparison, rankings are also provided based on traditional JCR impact factor. To save printing space, only the top ten journals are listed in Table 3. The rankings for all the 227 journals are listed in the Appendix-2. As we can see from Table 3 that the two rankings overlapped in 8 of the top 10 journals (80%), except that orders of some journals were different. This fact indicates that IF9 is basically consistent with the JCR impact factor, confirming the observation in Fig. 1 In the analysis above, we show that with these journals, IF9 has a one-to-one correspondence, whereas the JCR impact factor has a one-to-multiple correspondence. This is due to the fact that the JCR impact factor does not possess the ability to discriminate the shapes of the citation distribution functions, whereas the shapes of the citation distribution curves are properly taken into account by IF9. As a consequence, the JCR impact factor as an index of citations per publication usually rewards low productivity, and penalizes high productivity 6 .

Discussion
The JCR impact factor is the averaged number of citations received per publication. As pointed out by Hirsch 6 , measuring the average citations per publication, as does the JCR impact factor, usually rewards low productivity, and penalizes high productivity. This is  The data are derived from the Appendix-1, where C h-core , P, C total, e, t, r and IF9 are the citations within the h-core, the number of publications, the total citations, the e-index, the t-index, the head-tail ratio, and IF9, respectively. The head-tail ratio r and IF9 are defined in eqs. (1) and (2) Table 2. Their citation distribution curves are shown in Fig. 2. Note that the shapes of the two curves are different, as clearly shown in Fig. 2. The shape of the citation distribution curve for JPB is relatively sharp, whereas that for JLR is relatively flat. Unfortunately, the JCR impact factor cannot distinguish between the two cases, resulting in almost identical impact factor values (1.711 vs. 1.707). On the contrary, IF9 is able to distinguish between the academic performance of the two journals,resulting in the values of IF9 (3.658 vs.1.867).This example shows that IF9 results in distinct values for different journal citation distributions, whereas different citation distribution curves may correspond to the same JCR impact factor value. In other words, IF9 and journals have a relation of oneto-one correspondence, whereas the JCR impact factor and journals have a relation of one-to-multiple correspondence. Table 2 shows that in addition to the numbers of publication, the total citations, the average citations per publication (i.e., the JCR impact factor) and the h-indices are all roughly equal to each other for the two journals. Of note, the four indices mentioned above are all the single-number evaluation indices currently available and widely used nowadays. Unfortunately, none of them is capable of discriminating the academic performance of the two journals. On the contrary, IF9 (or the h9-index) is a single-number evaluation index that is able to distinguish between the academic performance of journals with different citation distribution. In addition to the two journals mentioned above, other three similar pairs of journals are also listed in Table 2.
Of note, the example above is a typical case, rather than a rare event, because we can find a number of similar cases, as shown in  Note that the citation distribution curve for the journal JPB is relatively peaked, indicating that a part of its publications are highly cited, whereas that for the journal JLR is relatively flat, indicating that most of its publications are relatively lowly cited. Although the total citations are approximately equal, the academic performance of the two journals is different. The JCR impact factor cannot distinguish between the two journals, with almost identical JCR impact factor IF < 1.7. On the contrary, IF9 possesses the ability to distinguish between the two journals with IF9 < 3.6 and IF9 < 1.8 for JPB and JLR, respectively.  Table 2. Let us further consider two or more journals with roughly equal JCR impact factors, but the numbers of publication may be different. Such cases occur more frequently than the example shown above. Although their JCR impact factors are roughly equal, their citation distribution curves may be different, even quite different. The traditional JCR impact factor lacks the ability to discriminate different shapes of the citation distribution curves, whereas IF9 proposed in this paper does not have this drawback. In this regard, IF9 is an alternative to the JCR impact factor with unique features that reward journals with highly-cited papers, but disregard lowly-cited papers. We need to point out that whether journals with such peaked citation distribution are preferable to those having uniform distribution is arguable. However, current studies on the citation distributions show that the citation distributions obey the so-called power law [24][25][26] , stretched exponential 24,27,28 , lognormal 24,29-31 and modified Bessel function 24,32 . According to the parameters involved in these functions, the citation distributions are usually skewed, rather than uniform.
In summary, IF9 is proposed as an alternative to the JCR impact factor with some unique features. (i) IF9 is designed to possess the ability to distinguish between different shapes of the citation distribution curves. It gives larger values of IF9 to those with relatively sharp citation distribution curves, whereas lower values to those with flat ones. This is in agreement with the common point of view of academic evaluation 33,34 . (ii) Citation information of three years is considered by IF9, rather than 2 years for JCR impact factor, and therefore IF9 carries more citation information. (iii) IF9 is basically consistent with the JCR impact factor, and the two impact factors have roughly the same order of magnitude. These features make IF9 relatively easy to be accepted by the academic community. IF9 may properly reflect the academic performance of a scientific journal in a way that is different from the JCR impact factor with some unique features that reward journals with highly cited papers, and therefore it could be used to complement the JCR impact factor.

Methods
As an example, the journals in the category of biochemistry and molecular biology were studied. According to the Thomson Reuters Journal Citation Reports (JCR) Science Edition 2011, there are 290 journals listed in the subject category BIOCHEMISTRY & MOLECULAR BIOLOGY. Among these 290 journals, a few of them changed their titles during the period of 2006 to 2010. Some journals published fewer than 100 articles, whereas some were not continuously indexed by the Web of Science database (WoS) during the period of 2006-2010. All the journals mentioned above were excluded from the current study. Consequently, 227 journals were remained for the present study. We downloaded the Journal Summary List of the subject category BIOCHEMISTRY & MOLECULAR BIOLOGY in the JCR Science Edition 2011 and extracted the Impact Factor values of the 227 journals. The detailed titles and related data for the 227 journals are listed in the Appendix-1.