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Representative Points from a Mixture of Two Normal Distributions

Author

Listed:
  • Yinan Li

    (Department of Statistics and Data Science, Beijing Normal University–Hong Kong Baptist University United International College, Zhuhai 519087, China
    Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong)

  • Kai-Tai Fang

    (Department of Statistics and Data Science, Beijing Normal University–Hong Kong Baptist University United International College, Zhuhai 519087, China
    The Key Lab of Random Complex Structures and Data Analysis, The Chinese Academy of Sciences, Beijing 100045, China)

  • Ping He

    (Department of Statistics and Data Science, Beijing Normal University–Hong Kong Baptist University United International College, Zhuhai 519087, China)

  • Heng Peng

    (Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong)

Abstract

In recent years, the mixture of two-component normal distributions (MixN) has attracted considerable interest due to its flexibility in capturing a variety of density shapes. In this paper, we investigate the problem of discretizing a MixN by a fixed number of points under the minimum mean squared error (MSE-RPs). Motivated by the Fang-He algorithm, we provide an effective computational procedure with high precision for generating numerical approximations of MSE-RPs from a MixN. We have explored the properties of the nonlinear system used to generate MSE-RPs and demonstrated the convergence of the procedure. In numerical studies, the proposed computation procedure is compared with the k -means algorithm. From an application perspective, MSE-RPs have potential advantages in statistical inference.Our numerical studies show that MSE-RPs can significantly improve Kernel density estimation.

Suggested Citation

  • Yinan Li & Kai-Tai Fang & Ping He & Heng Peng, 2022. "Representative Points from a Mixture of Two Normal Distributions," Mathematics, MDPI, vol. 10(21), pages 1-28, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3952-:d:951972
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    References listed on IDEAS

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    Cited by:

    1. Xiao Ke & Sirao Wang & Min Zhou & Huajun Ye, 2023. "New Approaches on Parameter Estimation of the Gamma Distribution," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    2. Kai-Tai Fang & Jianxin Pan, 2023. "A Review of Representative Points of Statistical Distributions and Their Applications," Mathematics, MDPI, vol. 11(13), pages 1-25, June.

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