Given a sequence of \(n\) non-negative numbers \(x=(x_1,\dots,x_n)\), where \(x_i \ge x_j \ge 0\) for \(i \le j\), the \(g\)-index (Egghe, 2006) for \(x\) is defined as $$G(x)=\max\{i=1,\dots,n: \sum_{j=1}^i x_i \ge i^2\}$$ if \(n \ge 1\) and \(x_1 \ge 1\), or \(G(x)=0\) otherwise.
index_g(x)index.g(x) # same as index_g(x), deprecated alias
index_g_zi(x)
a single numeric value
a non-negative numeric vector
index.g is a (deprecated) alias for index_g.
Note that index_g is not a zero-insensitive impact function,
see Examples section. index_g_zi is its zero-sensitive variant:
it assumes that the aggregated vector is padded with zeros.
If a non-increasingly sorted vector is given, the function has O(n) run-time.
For historical reasons, this function is also available via an alias,
index.g [but its usage is deprecated].
Egghe L., Theory and practise of the g-index, Scientometrics 69(1), 2006, pp. 131-152.
Mesiar R., Gagolewski M., H-index and other Sugeno integrals: Some defects and their compensation, IEEE Transactions on Fuzzy Systems 24(6), 2016, pp. 1668-1672. doi:10.1109/TFUZZ.2016.2516579
Gagolewski M., Mesiar R., Monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem, Information Sciences 263, 2014, pp. 166-174. doi:10.1016/j.ins.2013.12.004
Gagolewski M., Data Fusion: Theory, Methods, and Applications, Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp. isbn:978-83-63159-20-7
Other impact_functions:
index_h(),
index_lp(),
index_maxprod(),
index_rp(),
index_w(),
pord_weakdom()
sapply(list(c(9), c(9,0), c(9,0,0), c(9,0,0,0)), index_g) # not a zero-sensitive agop
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