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

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2 Citations (Scopus)

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

Fingerprint

Survival Function
Increasing Failure Rate
Product Measure
Gamma function
Rate Function
Weibull
Level Set
Density Function
Theorem

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

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title = "INTERRELATIONSHIPS BETWEEN lP‐ISOTROPIC DENSITIES AND lP‐ISOTROPIC SURVIVAL FUNCTIONS, AND DE FINETTI REPRESENTATIONS OF SCHUR‐CONCAVE SURVIVAL FUNCTIONS",
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.",
keywords = "de Finetti representation, l‐isotropy, level sets, log‐concave survival functions, Schur‐concavity",
author = "Yu Hayakawa",
year = "1993",
doi = "10.1111/j.1467-842X.1993.tb01340.x",
language = "English",
volume = "35",
pages = "327--332",
journal = "Australian and New Zealand Journal of Statistics",
issn = "1369-1473",
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T1 - INTERRELATIONSHIPS BETWEEN lP‐ISOTROPIC DENSITIES AND lP‐ISOTROPIC SURVIVAL FUNCTIONS, AND DE FINETTI REPRESENTATIONS OF SCHUR‐CONCAVE SURVIVAL FUNCTIONS

AU - Hayakawa, Yu

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

KW - de Finetti representation

KW - l‐isotropy

KW - level sets

KW - log‐concave survival functions

KW - Schur‐concavity

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JO - Australian and New Zealand Journal of Statistics

JF - Australian and New Zealand Journal of Statistics

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