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  Volume 9, Issue 1, Article 13
A Functional Inequality for the Survival Function of the Gamma Distribution

    Authors: Árpád Baricz,  
    Keywords: Error function; Incomplete gamma function; Density function; Survival function; Complete monotonicity; Functional inequality; New-is-better-than-used property; Log-concavity.  
    Date Received: 12/01/08  
    Date Accepted: 18/02/08  
    Subject Codes:

33B20, 26D05.

    Editors: Andrea Laforgia,  

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-Mitrinovic inequality.

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