The b-index (Brown 2009) is designed to correct h for self-citations, without actually having to check the citation records for every publication. It assumes that an author's self-citation rate is fairly consistent across publications such that, on average, a fraction k of the citations are from other authors. Assuming that citations follow a Zipfian distribution and that empirically derived estimates of the shape of this distribution are reasonable, one finds the index
where b is an estimate of the h-index corrected for self-citations.
There are multiple ways to estimate the non-self-citation rate (k). In this case, we calculate it directly as the mean of the proportion of self and coauthor-citations to total-citations across all publication, subtracted from one, or