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A Comparison of MLE for Some Index Distributions Based on Censored Samples

Author

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  • Yunhan Liu

    (Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China
    These authors contributed equally to this work.)

  • Changchun Gao

    (Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China
    These authors contributed equally to this work.)

  • Xiaofeng Liu

    (Department of Statistics, Shanghai University of Finance and Economics Zhejiang College, Jinhua 321000, China
    These authors contributed equally to this work.)

  • Ping Luo

    (Department of Statistics, Shanghai University of Finance and Economics Zhejiang College, Jinhua 321000, China
    These authors contributed equally to this work.)

  • Jianguo Ren

    (Department of Mathematics, Shanghai University of Finance and Economics Zhejiang College, Jinhua 321000, China
    These authors contributed equally to this work.)

Abstract

This paper elucidates the prerequisites for maximum likelihood estimation (MLE) of parameters within the exponential and scale parameter families. Estimation of these parameters is predicated on data derived from censored samples and seeks to adhere to stochastic ordering principles. The study establishes that for two independent normal distributions and a two-parameter exponential distribution discernible by the distinct parameter sets, the MLEs of the parameters evince a stochastically ordered relationship when evaluated using full datasets. Furthermore, this research is extended to corroborate the persistence of stochastic ordering in the MLEs of such parameters under conditions of fixed censoring of samples.

Suggested Citation

  • Yunhan Liu & Changchun Gao & Xiaofeng Liu & Ping Luo & Jianguo Ren, 2024. "A Comparison of MLE for Some Index Distributions Based on Censored Samples," Mathematics, MDPI, vol. 12(20), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3264-:d:1501136
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    References listed on IDEAS

    as
    1. Fanhui Kong & Heliang Fei, 1996. "Limit theorems for the maximum likelihood estimate under general multiply Type II censoring," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 731-755, December.
    2. Guoxin Qiu & Mohammad Z. Raqab, 2024. "On weighted extropy of ranked set sampling and its comparison with simple random sampling counterpart," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(1), pages 378-395, January.
    3. Ya-Hsuan Hu & Takeshi Emura, 2015. "Maximum likelihood estimation for a special exponential family under random double-truncation," Computational Statistics, Springer, vol. 30(4), pages 1199-1229, December.
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