  The Birnbaum-Saunders distribution, also known as the fatigue-life
distribution, is frequently used in reliability studies. We obtain adjustments
to the Birnbaum--Saunders profile likelihood function. The modified versions of
the likelihood function were obtained for both the shape and scale parameters,
i.e., we take the shape parameter to be of interest and the scale parameter to
be of nuisance, and then consider the situation in which the interest lies in
performing inference on the scale parameter with the shape parameter entering
the modeling in nuisance fashion. Modified profile maximum likelihood
estimators are obtained by maximizing the corresponding adjusted likelihood
functions. We present numerical evidence on the finite sample behavior of the
different estimators and associated likelihood ratio tests. The results favor
the adjusted estimators and tests we propose. A novel aspect of the profile
likelihood adjustments obtained in this paper is that they yield improved point
estimators and tests. The two profile likelihood adjustments work well when
inference is made on the shape parameter, and one of them displays superior
behavior when it comes to performing hypothesis testing inference on the scale
parameter. Two empirical applications are briefly presented.
