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220 Becoming Metric-Wise

7.6 SOME OTHER H-TYPE INDICES
(2)
7.6.1 Kosmulski’s Index h
(2)
Kosmulski (2006) proposed the h -index in order to easily handle long
lists. An example could be download lists as studied in Hua et al. (2009).
(2)
The h -index is defined as follows: An author has a Kosmulski’s index
h (2) if r 5 h (2) is de highest rank such that the first h (2) articles have each at
(2) 2 (2)
least (h ) citations. The h -index for Table 7.2 is 2 as the first 2 articles
each have at least 4 citations, while the third does not have 9 citations.

7.6.2 The AR-index

In an attempt to design an h-type indicator that can actually decrease
over time and puts emphasis on recent publications Jin (2007) proposed
the AR-index. She defines the AR-index as the square root of the sum
of the average number of citations per year of articles included in the
h-core. As a formula this is:

v ffiffiffiffiffiffiffiffiffiffiffi
u
h
u X c i
AR 5 t (7.12)
a i
i51
where a i denotes the age (in years) of the i-th article. The AR-index is
clearly inspired by the R-index.

7.6.3 The m-index
Bornmann et al. (2008) propose the m-index (not to be confused with
Hirsch’s m-quotient, see Subsection 7.4.3), which is the median of the
items in the h-core. Being a median, it is less sensible to outliers than the
g-index or the R-index.

7.6.4 The h-index of a Single Publication
Schubert (2009) proposes an h-index for a single publication (the source)
as the h-index of the set of articles citing this source article. This means
the h-index of the set of all forward first generation i.e., citing publica-
tions (actually, he does not consider all publications, but only those of
article type).
We note that, when applied in a publication-citation context the
h-index and similar indices can be considered to be an impact indicator
as generally speaking many publications and many citations lead to a high