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INTERRELATIONSHIPS BETWEEN l P ‐ISOTROPIC DENSITIES AND l P ‐ISOTROPIC SURVIVAL FUNCTIONS, AND DE FINETTI REPRESENTATIONS OF SCHUR‐CONCAVE SURVIVAL FUNCTIONS
Author(s) -
Hayakawa Yu
Publication year - 1993
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1993.tb01340.x
Subject(s) - isotropy , weibull distribution , product (mathematics) , function (biology) , pure mathematics , survival function , mathematics , survival analysis , physics , geometry , statistics , quantum mechanics , biology , evolutionary biology
Summary Interrelationships between l P ‐isotropic densities and l P ‐isotropic survival functions are studied. We obtain representations for densities whose survival functions are l P ‐isotropic and for survival functions whose densities are l P ‐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.