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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41343

    Title: Inference for the extreme value distribution under progressive type-II censoring
    Authors: Balakrishnan, N.;Kannan, N.;Lin, C. T.;林千代;Wu, Sam S. J.
    Contributors: 淡江大學數學學系
    Keywords: Maximum likelihood estimator;Monte Carlo simulation;Pivotal quantity;Progressive Type-II censoring
    Date: 2004-01
    Issue Date: 2010-01-28 07:20:57 (UTC+8)
    Publisher: Taylor & Francis
    Abstract: The extreme value distribution has been extensively used to model natural phenomena such as rainfall and floods, and also in modeling lifetimes and material strengths. Maximum likelihood estimation (MLE) for the parameters of the extreme value distribution leads to likelihood equations that have to be solved numerically, even when the complete sample is available. In this paper, we discuss point and interval estimation based on progressively Type-II censored samples. Through an approximation in the likelihood equations, we obtain explicit estimators which are approximations to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using an iterative method and examine numerically their bias and mean squared error. The approximate estimators compare quite favorably to the MLEs in terms of both bias and efficiency. Results of the simulation study, however, show that the probability coverages of the pivotal quantities (for location and scale parameters) based on asymptotic normality are unsatisfactory for both these estimators and particularly so when the effective sample size is small. We, therefore, suggest the use of unconditional simulated percentage points of these pivotal quantities for the construction of confidence intervals. The results are presented for a wide range of sample sizes and different progressive censoring schemes. We conclude with an illustrative example.
    Relation: Journal of Statistical Computation and Simulation 74(1), pp.25-45
    DOI: 10.1080/0094965031000105881
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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