I would like to integrate a function with a random effect. The function is :
$G(t; \beta) = exp(- \lambda t^\gamma \exp(\beta Z))$,
$\beta$ being the random effect taken from a normal distribution of mean 0 and variance $\sigma$. The solution would be to make a double integration, first on $t$ and then over the distribution of the random effect.
But, I don't know ho to do in practice ! I am ready to use Monte-Carlo integration, I just need to calculate the area under the curve.
Any suggestion ?
Thanks a lot !