Hirsch's h-index

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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

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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.

See Also

Other impact_functions: index.g, index_g, index_g_zi; index.lp, index_lp; index.rp, index_rp; index_maxprod; index_w

Examples

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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)