Some Properties and Interval Estimation Based on Maximum Likelihood Estimators of the Crack Lifetime Distribution
The crack lifetime distribution is used for modeling lifetime data. This paper proposes some properties of the crack lifetime distribution. The confidence intervals of parameters based on the maximum likelihood estimators (MLEs) for crack lifetime distribution are considered. The Fisher information matrix is provided for constructing the asymptotic confidence interval. Moreover, the confidence intervals are computed using the two parametric bootstrap methods: the bootstrap-p and the bootstrap-t methods. Monte Carlo simulations are performed to investigate the performance of the three different interval estimation methods in terms of coverage probabilities and average width. Finally, a real data set is analyzed for illustrative purposes. Results indicate that the asymptotic confidence intervals behave very well for moderate and large sample sizes, while the bootstrap-p intervals work generally well. Moreover, the bootstrap-t intervals also perform quite satisfactorily for small sample sizes.
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