CITAN (version 2011.03-2)

index.rp: The $r_p$-index

Description

Computes the $r_p$-index of a numeric vector for given $p$.

Usage

index.rp(x, p=Inf, sorted.dec=FALSE, disable.check=FALSE)

Arguments

x
a non-negative numeric vector.
p
index order, $p \in [1,\infty]$; defaults $\infty$ (Inf).
sorted.dec
logical; TRUE if the vector has already been sorted non-increasingly; defaults FALSE.
disable.check
logical; TRUE to disable some validity checks on the input vector; defaults FALSE.

Value

  • The function returns a single number or NA if improper input has been given.

Details

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

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).

If disable.check is set to FALSE, then eventual NA values are removed from the input vector.

If a non-increasingly sorted vector is given as input (set sorted.dec to TRUE) the value of $r_\infty$ is calculated in log time (note that it may be determined in linear time using max(pmin(x, 1:length(x)))). Otherwise, linear time is needed.

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), 16569-16572, 2005. Woeginger G.J., An axiomatic characterization of the Hirsch-index, Mathematical Social Sciences, 56(2), 224-232, 2008.

See Also

index.h, index.g, index.lp, Sstat, Sstat2

Examples

Run this code
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}

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