IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v59y2018i1d10.1007_s00362-016-0751-1.html
   My bibliography  Save this article

Characterizations of the geometric distribution via residual lifetime

Author

Listed:
  • Nan-Cheng Su

    (National Taipei University)

  • Wan-Ping Hung

    (National Sun Yet-Sen University)

Abstract

In this work, some characterizations of the geometric distribution based on two kinds of residual lifetime are presented. Firstly we characterize geometric distribution by using certain relationships of moments of the truncated life from below, that is $$\max \{X-t,0\}$$ max { X - t , 0 } , where X is a positive integer-valued random variable. Secondly using certain relationships of moments of residual life $$\gamma _{t}$$ γ t at t of a renewal process, we characterize the common distribution of the inter-arrival times $$ \{X_{i},i\ge 1\}$$ { X i , i ≥ 1 } to be geometrically distributed when $$X_{1}$$ X 1 is also a positive integer-valued random variable.

Suggested Citation

  • Nan-Cheng Su & Wan-Ping Hung, 2018. "Characterizations of the geometric distribution via residual lifetime," Statistical Papers, Springer, vol. 59(1), pages 57-73, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0751-1
    DOI: 10.1007/s00362-016-0751-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0751-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-016-0751-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ramesh C. Gupta, 2006. "Variance residual life function in reliability studies," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 343-355.
    2. Kumar Kattumannil Sudheesh & N. Unnikrishnan Nair, 2010. "Characterization of discrete distributions by conditional variance," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 77-85.
    3. A. Dallas, 1979. "On the exponential law," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 26(1), pages 105-108, December.
    4. Roy, Dilip & Gupta, R. P., 1999. "Characterizations and model selections through reliability measures in the discrete case," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 197-206, June.
    5. Unnikrishnan Nair, N. & Sankaran, P.G., 2013. "Characterizations of discrete distributions using reliability concepts in reversed time," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1939-1945.
    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. Salehi, E.T. & Badía, F.G. & Asadi, M., 2012. "Preservation properties of a homogeneous Poisson process stopped at an independent random time," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 574-585.
    2. Szymkowiak, Magdalena & Iwińska, Maria, 2016. "Characterizations of Discrete Weibull related distributions," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 41-48.
    3. Arijit Patra & Chanchal Kundu, 2019. "On generalized orderings and ageing classes for residual life and inactivity time at random time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 691-704, August.
    4. Karlis, Dimitris & Patilea, Valentin, 2007. "Confidence intervals of the hazard rate function for discrete distributions using mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5388-5401, July.
    5. Jafar Ahmadi & H. N. Nagaraja, 2020. "Conditional properties of a random sample given an order statistic," Statistical Papers, Springer, vol. 61(5), pages 1971-1996, October.
    6. Sreehari M. & Sandhya E. & Mohamed Akbar V. K., 2018. "Some Reliability and Other Properties of Beta-Transformed Random Variables," Stochastics and Quality Control, De Gruyter, vol. 33(2), pages 83-92, December.
    7. Elham Khaleghpanah Noughabi & Majid Chahkandi & Majid Rezaei, 2022. "On the Mean and Variance Residual Life Comparisons of Coherent Systems with Identically Distributed Components," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2801-2822, December.
    8. Chanchal Kundu & Kshirod Sarkar, 2017. "Characterizations based on higher order and partial moments of inactivity time," Statistical Papers, Springer, vol. 58(3), pages 607-626, September.
    9. Francisco Germán Badía & María Dolores Berrade, 2022. "On the Residual Lifetime and Inactivity Time in Mixtures," Mathematics, MDPI, vol. 10(15), pages 1-20, August.
    10. M. Khorashadizadeh & A. Roknabadi & G. Borzadaran, 2013. "Variance residual life function based on double truncation," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 175-188, September.
    11. Wu, Jing & Qian, Cunhua & Dohi, Tadashi, 2024. "Optimal opportunity-based age replacement policies in discrete time," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    12. Arijit Patra & Chanchal Kundu, 2021. "Stochastic comparisons and ageing properties of residual lifetime mixture models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 123-143, August.
    13. N. Unnikrishnan Nair & P.G. Sankaran, 2010. "Properties of a mean residual life function arising from renewal theory," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(4), pages 373-379, June.
    14. Sarhan, Ammar M. & Kundu, Debasis, 2008. "Bayes estimators for reliability measures in geometric distribution model using masked system life test data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1821-1836, 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:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0751-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.