Inference on q-Weibull parameters

Xiang Jia, Saralees Nadarajah, Bo Guo

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    The q-Weibull distribution is a generalization of the Weibull distribution and could describe complex systems. We firstly point out how to derive the maximum likelihood estimates (MLEs) and least-squares estimates (LSEs) of the q-Weibull parameters. Next, three confidence intervals (CIs) for the q-Weibull parameters are constructed based on bootstrap methods and asymptotic normality of the MLEs. Explicit expressions for the Fisher information matrix necessary for the asymptotic CIs are derived. A Monte Carlo simulation study is conducted to compare the performances of the MLEs and LSEs as well as the different CIs. The simulation results show that the MLEs are superior to the LSEs in terms of both bias and mean squared error. The bootstrap CIs based on the MLEs are shown to have good coverage probabilities and average interval widths. Finally, a real data example is provided to illustrate the proposed methods.

    Original languageEnglish
    Pages (from-to)1-19
    Number of pages19
    JournalStatistical Papers
    Early online date21 Sept 2017
    Publication statusPublished - 2017


    • Confidence interval
    • Fisher information matrix
    • Least-squares estimate
    • Maximum likelihood estimate
    • q-Weibull distribution


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