# index_h: Hirsch's h-index In agop: Aggregation Operators and Preordered Sets

## Description

Given a sequence of n non-negative numbers x=(x_1,…,x_n), where x_i ≥ x_j ≥ 0 for i ≤ j, the h-index (Hirsch, 2005) for x is defined as

H(x)=max{i=1,…,n: x_i ≥ i}

if n ≥ 1 and x_1 ≥ 1, or H(x)=0 otherwise.

## Usage

 ```1 2 3``` ```index_h(x) index.h(x) # same as index_h(x), deprecated alias ```

## Arguments

 `x` a non-negative numeric vector

## Details

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

For historical reasons, this function is also available via its alias, `index.h` [but its usage is deprecated].

See `index_rp` and `owmax` for natural generalizations.

## Value

a single numeric value

## References

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

Other impact_functions: `index.g`, `index_g`, `index_g_zi`; `index.lp`, `index_lp`; `index.rp`, `index_rp`; `index_maxprod`; `index_w`
 ```1 2 3 4 5 6 7 8 9``` ```authors <- list( # a list of numeric sequences # (e.g. citation counts of the articles # written by some authors) "A" =c(23,21,4,2,1,0,0), "B" =c(11,5,4,4,3,2,2,2,2,2,1,1,1,0,0,0,0), "C" =c(53,43,32,23,14,13,12,8,4,3,2,1,0) ) index_h(authors\$A) sapply(authors, index_h) ```