In a paper[1] on generating survival data from a Cox proportional hazard model, they specify following cumulative distribution function:
\begin{equation} F(t^0) = \frac{1}{5}\sum_{x=0}^{4} \exp(-\exp(\beta x) t^0). \end{equation}
with $\beta = 0.5\log(2)$
They generate random numbers from this distribution but don't specify how.
I don't see a way to invert the distribution and inverse transform sampling.
How would you sample from this kind of distribution?
[1]: Mackenzie, Todd, and Michal Abrahamowicz. "Marginal and hazard ratio specific random data generation: applications to semi-parametric bootstrapping." Statistics and Computing 12.3 (2002): 245-252.