  We address the issue of performing inference on the parameters that index a
bimodal extension of the Birnbaum-Saunders distribution (BS). We show that
maximum likelihood point estimation can be problematic since the standard
nonlinear optimization algorithms may fail to converge. To deal with this
problem, we penalize the log-likelihood function. The numerical evidence we
present show that maximum likelihood estimation based on such penalized
function is made considerably more reliable. We also consider hypothesis
testing inference based on the penalized log-likelihood function. In
particular, we consider likelihood ratio, signed likelihood ratio, score and
Wald tests. Bootstrap-based testing inference is also considered. We use a
nonnested hypothesis test to distinguish between two bimodal BS laws. We derive
analytical corrections to some tests. Monte Carlo simulation results and
empirical applications are presented and discussed.
