index_g: Egghe's g-index

In agop: Aggregation Operators and Preordered Sets

Description

Given a sequence of n non-negative numbers x=(x_1,…,x_n), where x_i ≥ x_j ≥ 0 for i ≤ j, the g-index (Egghe, 2006) for x is defined as

G(x)=max{i=1,…,n: x_1+…+x_i ≥ i^2}

if n ≥ 1 and x_1 ≥ 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

agop documentation built on March 26, 2020, 7:48 p.m.