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New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme

Author

Listed:
  • Jung-In Seo

    (Division of Convergence Education, Halla University, Wonju-si, Gangwon-do 26404, Korea)

  • Young Eun Jeon

    (Department of Statistics, Yeungnam University, Gyeongsan-si, Gyeongsangbuk-do 38541, Korea)

  • Suk-Bok Kang

    (Department of Statistics, Yeungnam University, Gyeongsan-si, Gyeongsangbuk-do 38541, Korea)

Abstract

This paper proposes a new approach based on the regression framework employing a pivotal quantity to estimate unknown parameters of a Weibull distribution under the progressive Type-II censoring scheme, which provides a closed form solution for the shape parameter, unlike its maximum likelihood estimator counterpart. To resolve serious rounding errors for the exact mean and variance of the pivotal quantity, two different types of Taylor series expansion are applied, and the resulting performance is enhanced in terms of the mean square error and bias obtained through the Monte Carlo simulation. Finally, an actual application example, including a simple goodness-of-fit analysis of the actual test data based on the pivotal quantity, proves the feasibility and applicability of the proposed approach.

Suggested Citation

  • Jung-In Seo & Young Eun Jeon & Suk-Bok Kang, 2020. "New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme," Mathematics, MDPI, vol. 8(10), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1713-:d:423799
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    References listed on IDEAS

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    1. Pareek, Bhuvanesh & Kundu, Debasis & Kumar, Sumit, 2009. "On progressively censored competing risks data for Weibull distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4083-4094, October.
    2. Hai-Lin Lu & Shin-Hwa Tao, 2007. "The Estimation of Pareto Distribution by a Weighted Least Square Method," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(6), pages 913-926, December.
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