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New Approaches on Parameter Estimation of the Gamma Distribution

Author

Listed:
  • Xiao Ke

    (College of Big Data and Internet, Shenzhen Technology University, Shenzhen 518118, China)

  • Sirao Wang

    (Faculty of Science and Technology, BNU-HKBU United International College, Zhuhai 519087, China
    Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China
    Department of Mathematics, Hong Kong Baptist University, Hong Kong, China)

  • Min Zhou

    (Faculty of Science and Technology, BNU-HKBU United International College, Zhuhai 519087, China
    Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China)

  • Huajun Ye

    (Faculty of Science and Technology, BNU-HKBU United International College, Zhuhai 519087, China
    Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China)

Abstract

This paper discusses new approaches to parameter estimation of gamma distribution based on representative points. In the first part, the existence and uniqueness of gamma mean squared error representative points (MSE-RPs) are discussed theoretically. In the second part, by comparing three types of representative points, we show that gamma MSE-RPs perform well in parameter estimation and simulation. The last part proposes a new Harrel–Davis sample standardization technique. Simulation studies reveal that the standardized samples can be used to improve estimation performance or generate MSE-RPs. In addition, a real data analysis illustrates that the proposed technique yields efficient estimates for gamma parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:927-:d:1065926
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    References listed on IDEAS

    as
    1. Long-Hao Xu & Kai-Tai Fang & Ping He, 2022. "Properties and generation of representative points of the exponential distribution," Statistical Papers, Springer, vol. 63(1), pages 197-223, February.
    2. Jiang, Jia-Jian & He, Ping & Fang, Kai-Tai, 2015. "An interesting property of the arcsine distribution and its applications," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 88-95.
    3. Santanu Chakraborty & Mrinal Kanti Roychowdhury & Josef Sifuentes, 2021. "High Precision Numerical Computation of Principal Points for Univariate Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 558-584, November.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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