index_g: Egghe's g-index

In Rexamine/agop: Aggregation Operators and Preordered Sets

Egghe's g-index

Description

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.

Usage

index_g(x)

index.g(x) # same as index_g(x), deprecated alias

index_g_zi(x)

Arguments

x	a non-negative numeric vector

Details

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].

Value

a single numeric value

References

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

See Also

Other impact_functions: index_h(), index_lp(), index_maxprod(), index_rp(), index_w(), pord_weakdom()

Examples

sapply(list(c(9), c(9,0), c(9,0,0), c(9,0,0,0)), index_g) # not a zero-sensitive agop

Rexamine/agop documentation built on Dec. 11, 2023, 10:02 p.m.