A functional inequality for the survival function of the gamma distribution

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8 Citations (Scopus)

Abstract

In this note we give a completely different proof to a functional inequality established by Ismail and Laforgia for the survival function of the gamma distribution and we show that the inequality in the question is in fact the so-called new-is-better-than-used property, which arises in economic theory. Moreover, we extend this result to arbitrary reliability functions and we present a new simple proof for the Esseen-Mitrinović inequality.

Original languageEnglish
Article number13
JournalJournal of Inequalities in Pure and Applied Mathematics
Volume9
Issue number1
Publication statusPublished - 2008

Fingerprint

Functional Inequalities
Survival Function
Gamma distribution
Reliability Function
Economics
Arbitrary

Keywords

  • Complete monotonicity
  • Density function
  • Error function
  • Functional inequality
  • Incomplete gamma function
  • Log-concavity
  • New-is-better-than-used property
  • Survival function

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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KW - Complete monotonicity

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KW - Incomplete gamma function

KW - Log-concavity

KW - New-is-better-than-used property

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