### 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 language | English |
---|---|

Article number | 13 |

Journal | Journal of Inequalities in Pure and Applied Mathematics |

Volume | 9 |

Issue number | 1 |

Publication status | Published - 2008 |

### Fingerprint

### 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

**A functional inequality for the survival function of the gamma distribution.** / Baricz, Árpád.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A functional inequality for the survival function of the gamma distribution

AU - Baricz, Árpád

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Complete monotonicity

KW - Density function

KW - Error function

KW - Functional inequality

KW - Incomplete gamma function

KW - Log-concavity

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

KW - Survival function

UR - http://www.scopus.com/inward/record.url?scp=42949130596&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42949130596&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:42949130596

VL - 9

JO - Journal of Inequalities in Pure and Applied Mathematics

JF - Journal of Inequalities in Pure and Applied Mathematics

SN - 1443-5756

IS - 1

M1 - 13

ER -