I have convinced myself that the geometric mean of a sample from a gamma
distribution with parameter alpha (i.e. arithmetic mean = variance = alpha)
has expectation (alpha-0.5) for alpha>5 or so, based on the exponential of
the corresponding digamma function.
Can anyone show this identity algebraically? I couldn't see it in
Abramowitz and Stegun.
Tim Cole
[log in to unmask] Phone +44(0)20 7905 2666 Fax +44(0)20 7242 2723
Epidemiology & Public Health, Institute of Child Health, London WC1N 1EH, UK
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|