Sharp estimates for the median of the [Gamma](n+1,1) distribution

José A. Adell and Pedro Jodrá

Statistics & Probability Letters, 2005, vol. 71, issue 2, 185-191

Abstract: We give sharp upper and lower bounds for the median of the [Gamma](n+1,1) distribution, thus providing an immediate proof of two conjectures by Chen and Rubin (Statist. Probab. Lett. 4 (1986) 281) referring to the median of the Poisson distribution. Our approach uses a differential calculus for nonnecessarily smooth functions of the standard Poisson process and the central limit theorem.

Keywords: Central; limit; theorem; Charlier; polynomials; Gamma; distribution; Median; Poisson; process; Taylor's; formula (search for similar items in EconPapers)
Date: 2005
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