Analysis of Type-Ⅱ censored data from the Kies distribution with classical and generalized approaches

Wei Liu; Liang Wang; Yuhlong Lio; Sanku Dey; Min Wu; Wei Liu; Liang Wang; Yuhlong Lio; Sanku Dey; Min Wu

doi:10.3934/math.20251208

AIMS Mathematics

2025, Volume 10, Issue 11: 27480-27512. doi: 10.3934/math.20251208

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Analysis of Type-Ⅱ censored data from the Kies distribution with classical and generalized approaches

1.
School of Mathematics, Yunnan Normal University, Kunming, China
2.
Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Yunnan Normal University, Kunming, China
3.
Department of Mathematical Sciences, University of South Dakota, Vermillion, SD, USA
4.
Department of Statistics, St. Anthony's College, Shillong, India
5.
School of Economics and Management, Shanghai Maritime University, Shanghai, China

Received: 15 September 2025 Revised: 28 October 2025 Accepted: 17 November 2025 Published: 25 November 2025
MSC : 62F01, 62N02

This paper investigated statistical inference for the Kies distribution under the Type-Ⅱ censoring scheme; specifically, classical and alternative generalized inferential approaches were proposed for parameter estimation. From the classical likelihood perspective, maximum likelihood estimators for unknown parameters were derived, and the existence and uniqueness of these estimators was also established. The corresponding asymptotic confidence intervals were constructed based on the observed Fisher information matrix. For comparison, an alternative generalized estimation method was conducted based on the constructed pivotal quantities. Finally, the performance of different estimation methods was evaluated via extensive simulation studies, and meanwhile, two real-world data examples were presented to illustrate the applications of the proposed methods.
- Kies distribution,
- Type-Ⅱ censoring,
- parameter estimation,
- maximum likelihood method,
- generalized method
Citation: Wei Liu, Liang Wang, Yuhlong Lio, Sanku Dey, Min Wu. Analysis of Type-Ⅱ censored data from the Kies distribution with classical and generalized approaches[J]. AIMS Mathematics, 2025, 10(11): 27480-27512. doi: 10.3934/math.20251208

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Abstract

This paper investigated statistical inference for the Kies distribution under the Type-Ⅱ censoring scheme; specifically, classical and alternative generalized inferential approaches were proposed for parameter estimation. From the classical likelihood perspective, maximum likelihood estimators for unknown parameters were derived, and the existence and uniqueness of these estimators was also established. The corresponding asymptotic confidence intervals were constructed based on the observed Fisher information matrix. For comparison, an alternative generalized estimation method was conducted based on the constructed pivotal quantities. Finally, the performance of different estimation methods was evaluated via extensive simulation studies, and meanwhile, two real-world data examples were presented to illustrate the applications of the proposed methods.

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