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 $$MAXPROD(x)=\max\{i x_i: i=1,\dots,n\}$$
index_maxprod(x)a single numeric value
a non-negative numeric vector
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.
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
Other impact_functions:
index_g(),
index_h(),
index_lp(),
index_rp(),
index_w(),
pord_weakdom()