  We present a method for computing the likelihood of a mixed hitting-time
model that specifies durations as the first time a latent L\'evy process
crosses a heterogeneous threshold. This likelihood is not generally known in
closed form, but its Laplace transform is. Our approach to its computation
relies on numerical methods for inverting Laplace transforms that exploit
special properties of the first passage times of L\'evy processes. We use our
method to implement a maximum likelihood estimator of the mixed hitting-time
model in MATLAB. We illustrate the application of this estimator with an
analysis of Kennan's (1985) strike data.
