Robust Estimation of the Location Parameter of Life Distributions

摘要

This thesis determined that for time to failure distributions that are moderate deviations from the negative exponential distribution, a robust estimate of the minimum life could be arrived at by assuming the underlying distribution was exponential and using the minimum variance, unbiased, maximum likelihood estimator. It was found that estimators using the minimum distance statistics of Kolmogorov, Cramer-von Mises, and Anderson-Darling did not perform well with the asymmetric distributions explored in this thesis. However, they may still prove useful for life distributions with larger shape parameters. The analysis was accomplished by using Monte Carlo techniques to generate random samples of time to failure data from specific distributions, and using this empirical data to estimate the actual minimum life of the distribution. Five estimators were explored: the minimum variance, unbiased, maximum likelihood estimator of the two-parameter negative exponential distribution; the first ordered statistic; and the three minimum distance methods. The performance of these estimators was evaluated by comparing their mean square errors with the mean square error of the chosen best estimator.