INTERRELATIONSHIPS BETWEEN lP‐ISOTROPIC DENSITIES AND lP‐ISOTROPIC SURVIVAL FUNCTIONS, AND DE FINETTI REPRESENTATIONS OF SCHUR‐CONCAVE SURVIVAL FUNCTIONS

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Abstract

Interrelationships between lP‐isotropic densities and lP‐isotropic survival functions are studied. We obtain representations for densities whose survival functions are lP‐isotropic and for survival functions whose densities are lP‐isotiopic. The former are mixtures of products of Weibull densities and the latter are mixtures of products of Gamma survival functions. Based on a theorem proved by Cooke, we show that de Finetti representations for Schur‐concave survival functions that have the same level sets as a product measure can be represented as mixtures of products of increasing failure rate survival functions.

Original languageEnglish
Pages (from-to)327-332
Number of pages6
JournalAustralian Journal of Statistics
Volume35
Issue number3
DOIs
Publication statusPublished - 1993
Externally publishedYes

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Keywords

  • de Finetti representation
  • l‐isotropy
  • level sets
  • log‐concave survival functions
  • Schur‐concavity

ASJC Scopus subject areas

  • Statistics and Probability

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