index_maxprod {agop}

Kosmulski's MAXPROD-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 MAXPROD-index (Kosmulski, 2007) for x is defined as

MAXPROD(x)=\max\{i x_i: i=1,\dots,n\}

Usage

index_maxprod(x)

Arguments

x

a non-negative numeric vector

Details

If a non-increasingly sorted vector is given, the function has O(n) run-time.

The MAXPROD index is the same as the discrete Shilkret integral of x w.r.t. the counting measure.

See index_lp for a natural generalization.

Value

a single numeric value

References

Kosmulski M., MAXPROD - A new index for assessment of the scientific output of an individual, and a comparison with the h-index, Cybermetrics 11(1), 2007.

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_g(), index_h(), index_lp(), index_rp(), index_w(), pord_weakdom()