Reconsider the Weibull-gamma model of Section 18.2.3 after replacing the gamma distributed heterogeneity assumption by the assumption that heterogeneity is distributed according to the log-normal distribution with unit mean.

(a) Verify that in this case an analytical expression for the unconditional hazard function is not obtainable.

(b) Substitute the integral expression for unconditional hazard into the loglikelihood given in Section 17.6.3. Using the simulation-based maximum likelihood approach of Section 12.4, describe an estimation algorithm that details the various steps involved in likelihood maximization.