Inequalities for the median of the gamma distribution

Authors:
José A. Adell;Horst Alzer
Affiliations:
Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain;Morsbacher Str. 10, 51545 Waldbröl, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We provide several new inequalities involving @l"n, the median of the gamma distribution of order n+1 with parameter 1. Among others, we present sharp upper and lower bounds for the arithmetic mean of @l"1,@l"2,...,@l"n. For all integers n=1 we have @an+76+n2+8405H"nn