RANGE OF VALIDITY OF ALPHA AND BETA FOR A GENERALIZED DIVERSITY INDEXH(ALPHA,BETA) DUE TO GOOD

Authors
BACZKOWSKI AJ JOANES DN SHAMIA GM
Citation
Aj. Baczkowski et al., RANGE OF VALIDITY OF ALPHA AND BETA FOR A GENERALIZED DIVERSITY INDEXH(ALPHA,BETA) DUE TO GOOD, Mathematical biosciences, 148(2), 1998, pp. 115-128
Citations number
27
Categorie Soggetti
Mathematics, Miscellaneous","Mathematics, Miscellaneous","Biology Miscellaneous
Journal title
Mathematical biosciences → ACNP
ISSN journal
00255564
Volume
148
Issue
2
Year of publication
1998
Pages
115 - 128
Database
ISI
SICI code
0025-5564(1998)148:2<115:ROVOAA>2.0.ZU;2-U
Abstract
Good (I.J. Good, Biometrika 40 (1953) 237; J. Am. Statist. Assoc. 77 ( 1982) 561) proposed a diversity index H(alpha, beta), defined for non- negative integer alpha and beta, which generalized the well-known indi ces of Shannon and Simpson. In this paper we further generalize Good's index by allowing the parameters alpha and beta to take values in the real plane. For two simple properties which a 'good' diversity index should possess, we determine the range of valid alpha and beta values for this generalized index. (C) 1998 Elsevier Science Inc. All rights reserved.