IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i2p216-d318190.html
   My bibliography  Save this article

Detecting Extreme Values with Order Statistics in Samples from Continuous Distributions

Author

Listed:
  • Lorentz Jäntschi

    (Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania
    Institute of Doctoral Studies, Babeş-Bolyai University, 400091 Cluj-Napoca, Romania)

Abstract

In the subject of statistics for engineering, physics, computer science, chemistry, and earth sciences, one of the sampling challenges is the accuracy, or, in other words, how representative the sample is of the population from which it was drawn. A series of statistics were developed to measure the departure between the population (theoretical) and the sample (observed) distributions. Another connected issue is the presence of extreme values—possible observations that may have been wrongly collected—which do not belong to the population selected for study. By subjecting those two issues to study, we hereby propose a new statistic for assessing the quality of sampling intended to be used for any continuous distribution. Depending on the sample size, the proposed statistic is operational for known distributions (with a known probability density function) and provides the risk of being in error while assuming that a certain sample has been drawn from a population. A strategy for sample analysis, by analyzing the information about quality of the sampling provided by the order statistics in use, is proposed. A case study was conducted assessing the quality of sampling for ten cases, the latter being used to provide a pattern analysis of the statistics.

Suggested Citation

  • Lorentz Jäntschi, 2020. "Detecting Extreme Values with Order Statistics in Samples from Continuous Distributions," Mathematics, MDPI, vol. 8(2), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:216-:d:318190
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/2/216/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/2/216/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lorentz Jäntschi & Sorana D. Bolboacă, 2018. "Computation of Probability Associated with Anderson–Darling Statistic," Mathematics, MDPI, vol. 6(6), pages 1-17, May.
    2. Kaizhi Liang & Zhaosheng Zhang & Peng Liu & Zhenpo Wang & Shangfeng Jiang, 2019. "Data-Driven Ohmic Resistance Estimation of Battery Packs for Electric Vehicles," Energies, MDPI, vol. 12(24), pages 1-17, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhaosheng Zhang & Shuo Wang & Ni Lin & Zhenpo Wang & Peng Liu, 2023. "State of Health Estimation of Lithium-Ion Batteries in Electric Vehicles Based on Regional Capacity and LGBM," Sustainability, MDPI, vol. 15(3), pages 1-20, January.
    2. Robert Parham, 2023. "The Difference-of-Log-Normals Distribution: Properties, Estimation, and Growth," Papers 2302.02486, arXiv.org.
    3. Huertas, José I. & Serrano-Guevara, Oscar & Díaz-Ramírez, Jenny & Prato, Daniel & Tabares, Lina, 2022. "Real vehicle fuel consumption in logistic corridors," Applied Energy, Elsevier, vol. 314(C).
    4. Calum Strange & Shawn Li & Richard Gilchrist & Gonçalo dos Reis, 2021. "Elbows of Internal Resistance Rise Curves in Li-Ion Cells," Energies, MDPI, vol. 14(4), pages 1-15, February.
    5. Yan Ding & Zhe Ji & Peng Liu & Zhiqiang Wu & Gang Li & Dingsong Cui & Yizhong Wu & Sha Xu, 2021. "Gas Station Recognition Method Based on Monitoring Data of Heavy-Duty Vehicles," Energies, MDPI, vol. 14(23), pages 1-13, November.
    6. Dominik Dvorak & Daniele Basciotti & Imre Gellai, 2020. "Demand-Based Control Design for Efficient Heat Pump Operation of Electric Vehicles," Energies, MDPI, vol. 13(20), pages 1-18, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:216-:d:318190. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.