A note concerning multivariate total positivity on the simplex
- Univ. of Kentucky, Lexington, KY (United States)
Although compositional data arise frequently in many different disciplines, relatively little is known about families of parametric densities that reside on a simplex, which is the natural sample space for such data. An exception to this is a recent paper by Gupta and Richards wherein the Liouville family is defined and discussed. They sought to characterize dependence properties within this new family using, among other ideas, multivariate total positivity. Further investigation reveals that their results are not very useful. In fact, it is shown that there does not exist a Liouville density, as defined by Gupta and Richards, that is also multivariate totally positive of order 2. Fatal flaws associated with an obvious alternative to their definition are discussed.
- OSTI ID:
- 505184
- Report Number(s):
- CONF-9207256-Vol.79; CNN: Grant ATM-9108177; TRN: 97:003314-0017
- Resource Relation:
- Conference: IMA summer program on mathematical, computational, and statistical analyses in environmental studies, Minneapolis, MN (United States), 6-31 Jul 1992; Other Information: PBD: 1996; Related Information: Is Part Of Environmental studies: Mathematical, computational, and statistical analysis; Wheeler, M.F. [ed.] [Rice Univ., Houston, TX (United States)]; PB: 414 p.
- Country of Publication:
- United States
- Language:
- English
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