On the medians of gamma distributions and an equation of Ramanujan

Author:
K. P. Choi

Journal:
Proc. Amer. Math. Soc. **121** (1994), 245-251

MSC:
Primary 62E15; Secondary 33B15, 41A58

DOI:
https://doi.org/10.1090/S0002-9939-1994-1195477-8

MathSciNet review:
1195477

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Abstract | References | Similar Articles | Additional Information

Abstract: For , let denote the median of the distribution. We prove that . These bounds are sharp. There is an intimate relationship between and an equation of Ramanujan. Based on this relationship, we derive the asymptotic expansion of as follows:

Let median denote the median of a Poisson random variable with mean , where the median is defined to be the least integer *m* such that . We show that the bounds on imply

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1195477-8

Keywords:
Median,
Gamma distribution,
Poisson distribution,
chi-square distribution,
Poisson-Gamma relation,
Ramanujan's equation

Article copyright:
© Copyright 1994
American Mathematical Society