index_rp {agop} | R Documentation |
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, |
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