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

Jung-In Seo, Young Eun Jeon and Suk-Bok Kang
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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

Mathematics, 2020, vol. 8, issue 10, 1-10

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.

Keywords: pivotal quantity; progressive Type-II censored data; Weibull distribution; weighted least squares estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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