IDEAS home Printed from https://ideas.repec.org/p/iik/wpaper/143.html
   My bibliography  Save this paper

On A Two-Parameter Discrete Distribution And Its Applications

Author

Listed:
  • Shovan Chowdhury

    (Indian Institute of Management Kozhikode)

  • Amitava Mukherjee

    (Indian Institute of Management Udaipur)

  • S. Chakraborti

    (University of AlabamaTuscaloosa, USA)

Abstract

Mukherjee and Chakraborti (2012) proposed a single distribution-free (nonparametric) Shewhart-type chart based on Lepage (1971) test statistic for simultaneously monitoring both the location and the scale parameters of a continuous distribution when both of these parameters are unknown. In the present work, we consider a single distribution-free CUSUM chart based on Lepage statistic, referred to as CUSUM-Lepage (CL) chart. Our proposed chart is nonparametric and therefore, in control (denoted IC) properties of the chart remain invariant and known for all continuous distributions. Control limits are tabulated for implementation in practice. The IC and out of control (denoted OOC) performance properties of the chart are investigated through simulation studies in terms of the average, the standard deviation, the median and some percentiles of the run length distribution. Detailed comparison with the Shewhart-type chart is presented. We also examine the effect of the reference value (k) of CUSUM chart on the performance of CL chart. The proposed chart is illustrated through a real data. Summary and conclusions are presented.

Suggested Citation

  • Shovan Chowdhury & Amitava Mukherjee & S. Chakraborti, 2014. "On A Two-Parameter Discrete Distribution And Its Applications," Working papers 143, Indian Institute of Management Kozhikode.
    • Handle: RePEc:iik:wpaper:143
    as

    Download full text from publisher

    File URL: https://iimk.ac.in/websiteadmin/FacultyPublications/Working%20Papers/143abs.pdf?t=24
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. David McDonald, 1990. "A cusum procedure based on sequential ranks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 627-646, October.
    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. Lombard, F. & Hawkins, Douglas M. & Potgieter, Cornelis J., 2017. "Sequential rank CUSUM charts for angular data," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 268-279.
    2. Yanhong Wu, 1996. "A less sensitive linear detector for the change point based on kernel smoothing method," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 43(1), pages 43-55, December.
    3. Chao Liu & Qingjie Xu & Ya Fan & Hao Wu & Jian Chen & Peng Lin, 2023. "Detection of Abnormal Data in GNSS Coordinate Series Based on an Improved Cumulative Sum," Sustainability, MDPI, vol. 15(9), pages 1-16, April.
    4. Du, Lilun & Wen, Mengtao, 2023. "False discovery rate approach to dynamic change detection," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    5. Chunguang Zhou & Changliang Zou & Yujuan Zhang & Zhaojun Wang, 2009. "Nonparametric control chart based on change-point model," Statistical Papers, Springer, vol. 50(1), pages 13-28, January.

    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:iik:wpaper:143. 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: Sudheesh Kumar (email available below). General contact details of provider: https://edirc.repec.org/data/iikmmin.html .

    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.