= Solution
For the stated scale-parameterisation of the <Weibull distribution>, its incubation <survivor function> is $S_T(s)=\exp[-(s/\lambda)^\kappa]$ for $s\geq0$, with $\lambda,\kappa>0$. The continuous <back-calculation of infection incidence> equation becomes
$$
\boxed{\mu(t)=\int_0^\infty h(t-s)\frac\kappa\lambda
\left(\frac s\lambda\right)^{\kappa-1}
\exp\!\left[-\left(\frac s\lambda\right)^\kappa\right]ds.}
$$
Set $h(t-s)=0$ before the infection process's start if one is specified. For the equal-width endpoint approximation, integrate the incubation density over each delay bin:
$$
q_\ell(\lambda,\kappa)
=\exp\!\left[-\left(\frac{(\ell-1)\Delta}\lambda\right)^\kappa\right]
-\exp\!\left[-\left(\frac{\ell\Delta}\lambda\right)^\kappa\right].
$$
Thus \b[the discrete Weibull equation is]
$$
\boxed{\mu_k(\theta,\lambda,\kappa)
=\sum_{i<k}h_i(\theta)q_{k-i}(\lambda,\kappa).}
$$
For unequal intervals replace $q_{k-i}$ by $S_T(\max\{0,t_{k-1}-t_i\})-S_T(\max\{0,t_k-t_i\})$. These are probabilities, not point evaluations of a density; no additional factor of $\Delta$ is needed after bin integration.
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