A methodological analysis of the normalisation, calibration and linearity of continuous diversity measures

The concepts of concentration and diversity play an important role in several fields of research. The existing indices in use are plagued by three deficiencies. They lack normalisation; they lack calibration; and their nonlinearity causes insufficient discrimination among related but dissimilar situations. After appraising the most common measures in light of these concepts, the paper shows how extant indices could be normalised and calibrated. In addition, we outline the general criteria for future diversity measures, and construct an intrinsically normalised, calibrated and linear one. A theoretical derivation is provided and a number of arguments and illustrative examples are included. We also discuss the limitations of continuous indices, including ours, and proffer some useful caveats.