... function[*]
The "G'' notation was adopted from Hernandez et al. (2000), see Sect. 6.1. 
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... random[*]
The assumption that no additional information is available is crucial: for example, if the star is located in a cluster whose HR diagram clearly outlines one of the older isochrones, one would not hesitate to assign the corresponding age also to this star. 
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... median[*]
We consistently use the median for the statistics, as it is much more robust than the mean value for the sometimes extremely skew error distributions. The median also has the important advantage of being invariant with respect to the arbitrary choice of variable considered, viz., $\tau$ rather than $\log\tau$. 
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... multiplication[*]
Such an ad hoc procedure can be theoretically motivated by the finite probability (of order $\sim $0.01) that the star is a non-member or outlier in some other sense. We have verified that the resulting estimate of the cluster age is quite insensitive to the value of this constant. 
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Copyright ESO 2005