Linking Diversity and Disparity Measures

Sahadeb Sarkar, Ayanendranath Basu

Abstract


The purpose of this paper is to examine links between the diversity measures (Patil and Taillie 1982) and the disparity measures (Lindsay 1994), quantities apparently developed for somewhat different purposes. We demonstrate that numerous diversity measures satisfying all the desirable criteria mentioned by Patil and Taillie can be defined by the generating functions of certain disparities and the associated residual adjustment functions. This provides the statistician and the ecologist a wide class of flexible indices for the statistical measurement of diversity.

Keywords


Divergence; Hellinger distance; Negative exponential disparity; Residual adjustment function; Species rarity

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DOI: http://dx.doi.org/10.18187/pjsor.v8i3.521

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Title

Linking Diversity and Disparity Measures

Keywords

Divergence; Hellinger distance; Negative exponential disparity; Residual adjustment function; Species rarity

Description

The purpose of this paper is to examine links between the diversity measures (Patil and Taillie 1982) and the disparity measures (Lindsay 1994), quantities apparently developed for somewhat different purposes. We demonstrate that numerous diversity measures satisfying all the desirable criteria mentioned by Patil and Taillie can be defined by the generating functions of certain disparities and the associated residual adjustment functions. This provides the statistician and the ecologist a wide class of flexible indices for the statistical measurement of diversity.

Date

2012-07-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 8. No. 3, 2012



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810