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Abstract
This thesis offers new estimators for the parameters of the linear failure rate and Birnbaum-Saunders distributions which perform better than the maximum likelihood estimators of these parameters in some smaller sample cases. The new estimators have lower absolute bias and mean squared error than the maximum likelihood estimators for certain parameter values and small sample sizes, with some of the proposed estimators performing better than others. Moreover, all of the new estimators are much easier to compute than the maximum likelihood estimators, and they are all of closed form.
Various scenarios having different parameter combinations and sample sizes are simulated via Monte Carlo methods and analyzed, to see which of the new methods or the maximum likelihood estimators perform best. We see that for both the linear failure rate and Birnbaum-Saunders distributions, at least one of the newly offered estimation methods is less biased and has lower mean squared error than the maximum likelihood estimators in many different scenarios having small samples, though it is known that the maximum likelihood estimators are the most asymptotically efficient for very large sample sizes.
