References
- Adell J.A. and Jodrá P. Sharp estimates for the median of the γ (n + 1, 1) distribution. Statist . Probab. Lett ., 71 2 : 185 – 191 , 2005 . http://dx.doi.org/10.1016/j.spl.2004.10.025 .
- J.A . Adel l and P . Jodrá . On a Ramanujan equation connected with the median of the Gamma distribution . Trans. Amer. Math. Soc ., 360 7 : 3631 – 3644 , 2008 . http://dx.doi.org/10.1090/S0002-9947-07-04411-X .
- S.E . Alm . Monotonicity of the difference between median and mean of gamma distributions and of a related Ramanujan sequence . Bernoulli , 9 2 : 351 – 371 , http://dx.doi.org/10.3150/bj/1068128981 .
- H . Alzer . Proof of the Chen–Rubin conjecture . Proc. Roy. Soc. Edinburgh Sect . 135 4 : 677 – 688 , 2005 . http://dx.doi.org/10.1017/S0308210500004066 .
- H . Alzer . A convexity property of the median of the gamma distribution . Statist. Probab. Lett ., 76 14 : 1510 – 1513 , 2006 . http://dx.doi.org/10.1016/j.spl.2006.03.011 .
- K.O . Bowman , L.R . Shenton and G . Szekeres . A Poisson sum up to the mean and a Ramanujan problem . J. Stat. Comput. Simul ., 20 2 : 167 – 173 , 1984 . http://dx.doi.org/10.1080/00949658408810769 .
- J . Chen and H . Rubin . Bounds for the difference between median and mean of Gamma and Poisson distributions . Statist. Probab. Lett ., 4 6 : 281 – 283 , 1986 . http://dx.doi.org/10.1016/0167-7152(86)90044-1 .
- Chihara , T.S. 1978 . An Introduction to Orthogonal Polynomials , New York : Gordon and Breach .
- K.P . Choi . On the medians of Gamma distributions and an equation of Ramanujan . Proc. Amer. Math. Soc ., 121 1 : 245 – 251 , 1994 . http://dx.doi.org/10.1090/S0002-9939-1994-1195477-8 .
- Heck , A. 2003 . Introduction to Maple , third edition , New York : Springer-Verlag .
- F . Jiméenez and P . Jodrá . On the computer generation of the Erlang and negative binomial distributions with shape parameter equal to two . Math. Comput. Simul ., 79 5 : 1636 – 1640 , 2009 . http://dx.doi.org/10.1016/j.matcom.2008.07.010 .
- J.C.W . Marsaglia . The incomplete Gamma function and Ramanujan's rational approximation to ex. J. Statis . Comput. Simul ., 24 2 : 163 – 168 , 1986 . http://dx.doi.org/10.1080/00949658608810899 .
- Ramanujan , S. 1911 . Question 294 . J. Indian Math. Soc. , 3 : 128
- Ramanujan , S. 1962 . Collected Papers , New York : Chelsea Publishing Co .