0
$\begingroup$

Hirsch index (one of the most popular citation indices) can be in fact calculated for any finite sequence/sample of natural numbers. Indeed, let $x_0, x_1,\ldots,x_{n-1}$ be a finite sequence of natural numbers. Without loss of generality we may assume that the sequence $(x_k)$ is decreasing. Then we define the Hirsch index of $(x_k)$ as the maximal natural number $h$ such that $ f(k) = x_k \geqslant k. $ (Thus $h$ is sort of the "fixed point" of the function $f$ defined in the last display).

I wonder are there nontrivial statements/results in probability and statistics involving the Hirsch index in the sense above?

1 Answers 1

1

Asking Math Reviews about the Hirsch index turns up two papers:

MR2442203 (2009f:91113)
Woeginger, Gerhard J.
An axiomatic characterization of the Hirsch-index.
Math. Social Sci. 56 (2008), no. 2, 224–232.

...In this paper, the author provides an axiomatic characterization of this index (i.e., a set of necessary and sufficient properties that uniquely identify the index) and proposes another index that should lead to a somewhat finer ranking than the Hirsch-index.
Reviewed by Maurice Salles

MR2724502 (2012b:62366)
Beirlant, Jan; Einmahl, John H. J.
Asymptotics for the Hirsch index.
Scand. J. Stat. 37 (2010), no. 3, 355–364.

The summary includes the statement, "In this article, we establish the asymptotic normality of the empirical $h$-index."

  • 0
    Gerry Myerson: Thank you.2012-06-24