index_rp {agop}

The r_p-index

Description

Given a sequence of n non-negative numbers x=(x_1,\dots,x_n), where x_i \ge x_j for i \le j, the r_p-index for p=\infty equals to

r_p(x)=\max_{i=1,\dots,n} \{ \min\{i,x_i\} \}

if n \ge 1, or r_\infty(x)=0 otherwise. That is, it is equivalent to a particular OWMax operator, see owmax.

For the definition of the r_p-index for p < \infty we refer to (Gagolewski, Grzegorzewski, 2009).

Usage

index_rp(x, p = Inf)

index.rp(x, p = Inf) # same as index_rp(x, p), deprecated alias

Arguments

x

a non-negative numeric vector

p

index order, p \in [1,\infty]; defaults \infty (Inf).

Details

Note that if x_1,\dots,x_n are integers, then

r_\infty(x)=H(x),

where H is the h-index (Hirsch, 2005) and

r_1(x)=W(x),

where W is the w-index (Woeginger, 2008), see index_h and index_w.

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.rp [but its usage is deprecated].

Value

a single numeric value

References

Gagolewski M., Grzegorzewski P., A geometric approach to the construction of scientific impact indices, Scientometrics 81(3), 2009, pp. 617-634.

Hirsch J.E., An index to quantify individual's scientific research output, Proceedings of the National Academy of Sciences 102(46), 2005, pp. 16569-16572.

Woeginger G.J., An axiomatic characterization of the Hirsch-index, Mathematical Social Sciences 56(2), 2008, pp. 224-232.

See Also

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

Examples

x <- runif(100, 0, 100);
index.rp(x);            # the r_oo-index
floor(index.rp(x));     # the h-index
index.rp(floor(x), 1);  # the w-index