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GompertzMakehamDistribution

represents a Gompertz-Makeham distribution.

$ wo 'GompertzMakehamDistribution[l, x0]'
GompertzMakehamDistribution[l, x0]

The two-argument (pure Gompertz) form has closed-form mean and median in terms of the incomplete gamma function Gamma[0, ΞΎ]:

$ wo 'Mean[GompertzMakehamDistribution[l, x]]'
(E^x*Gamma[0, x])/l

$ wo 'Median[GompertzMakehamDistribution[l, x]]'
Log[1 + Log[2]/x]/l