Sharp estimates for the median of the distribution

• DOI: 10.1016/j.spl.2004.10.025
• Publication Date: 2004-12-15T19:35:20Z
• Authors: José A. Adell; Pedro Jodrá
• Keywords: Central limit theorem

Abstract We give sharp upper and lower bounds for the median of the Γ ( 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.