Time Lagged Conversion Rates - Generalized Gamma(or something)

[robchadil]

I am currently implementing the Weibull cure fitter as documented in lifeline for time lagged conversion rates. I have been trying to implement a more flexible distribution (generalized gamma) that would fit my data better but I am unsure how to define the survival function and parameters for that distribution. This is how the weibull is defined sf = np.exp(-(T / lambda_) ** rho_) - how would I modify this to implement the GG?

I can see that scipy has a gengamma function but I would like to define the functional form similar to the weibull above.