IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i18p3847-d1235521.html
   My bibliography  Save this article

Discriminating among Generalized Exponential, Weighted Exponential and Weibull Distributions

Author

Listed:
  • Ruizheng Niu

    (School of Science, Xi’an University of Technology, Xi’an 710048, China)

  • Weizhong Tian

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

  • Yunchu Zhang

    (College of New Material and New Energy, Shenzhen Technology University, Shenzhen 518118, China)

Abstract

In this paper, we consider the problem of discriminating among three different positively skewed lifetime distributions, namely the generalized exponential distribution, the weighted exponential distribution, and the Weibull distribution. All of these distributions have been used quite effectively to analyze positively skewed lifetime data. We use the methods of the ratio of maximized likelihood, the minimum Kolmogorov distance, and the sequential probability ratio test to discriminate among these three distributions. The probability of correct selection is considered for each hypothesis based on several scenarios with Monte Carlo simulation. Real data applications are studied to illustrate the effectiveness of these proposed methods.

Suggested Citation

  • Ruizheng Niu & Weizhong Tian & Yunchu Zhang, 2023. "Discriminating among Generalized Exponential, Weighted Exponential and Weibull Distributions," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3847-:d:1235521
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/18/3847/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/18/3847/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gupta, Rameshwar D. & Kundu, Debasis, 2003. "Discriminating between Weibull and generalized exponential distributions," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 179-196, June.
    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. Zoran Vidović, 2019. "Bayesian Prediction of Order Statistics Based on k -Record Values from a Generalized Exponential Distribution," Stats, MDPI, vol. 2(4), pages 1-10, November.
    2. Chansoo Kim & Seongho Song, 2010. "Bayesian estimation of the parameters of the generalized exponential distribution from doubly censored samples," Statistical Papers, Springer, vol. 51(3), pages 583-597, September.
    3. E. M. Almetwally & H. M. Almongy & M. K. Rastogi & M. Ibrahim, 2020. "Maximum Product Spacing Estimation of Weibull Distribution Under Adaptive Type-II Progressive Censoring Schemes," Annals of Data Science, Springer, vol. 7(2), pages 257-279, June.
    4. Shovan Chowdhury, 2019. "Selection between Exponential and Lindley distributions," Working papers 316, Indian Institute of Management Kozhikode.
    5. Abdel-Hamid, Alaa H. & AL-Hussaini, Essam K., 2009. "Estimation in step-stress accelerated life tests for the exponentiated exponential distribution with type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1328-1338, February.
    6. Saieed Ateya, 2014. "Maximum likelihood estimation under a finite mixture of generalized exponential distributions based on censored data," Statistical Papers, Springer, vol. 55(2), pages 311-325, May.
    7. Chen, D.G. & Lio, Y.L., 2010. "Parameter estimations for generalized exponential distribution under progressive type-I interval censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1581-1591, June.
    8. Kim, Jin Seon & Yum, Bong-Jin, 2008. "Selection between Weibull and lognormal distributions: A comparative simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 477-485, December.
    9. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    10. Debasis Kundu & Anubhav Manglick, 2004. "Discriminating between the Weibull and log‐normal distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 893-905, September.
    11. Kundu, Debasis & Gupta, Rameshwar D., 2007. "A convenient way of generating gamma random variables using generalized exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2796-2802, March.
    12. David Han & Debasis Kundu, 2013. "Inference for a step-stress model with competing risks from the GE distribution under Type-I censoring," Working Papers 0181mss, College of Business, University of Texas at San Antonio.
    13. Nandi, Swagata & Dewan, Isha, 2010. "An EM algorithm for estimating the parameters of bivariate Weibull distribution under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1559-1569, June.
    14. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    15. Naresh Chandra Kabdwal & Qazi J. Azhad & Rashi Hora, 2024. "Statistical inference of the exponentiated exponential distribution based on progressive type-II censoring with optimal scheme," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(8), pages 3833-3853, August.
    16. Yu-Jau Lin & Y. L. Lio, 2012. "Bayesian inference under progressive type-I interval censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(8), pages 1811-1824, April.
    17. Heba S. Mohammed & Saieed F. Ateya & Essam K. AL-Hussaini, 2017. "Estimation based on progressive first-failure censoring from exponentiated exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1479-1494, June.
    18. Sarhan, Ammar M. & Balakrishnan, N., 2007. "A new class of bivariate distributions and its mixture," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1508-1527, August.
    19. Torabi, Hamzeh & Bagheri, F.L. & Mahmoudi, E., 2018. "Estimation of parameters for the Marshall–Olkin generalized exponential distribution based on complete data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 177-185.
    20. Ali Akbar Bromideh, 2012. "Discriminating Between Weibull and Log-Normal Distributions Based on Kullback-Leibler Divergence," Istanbul University Econometrics and Statistics e-Journal, Department of Econometrics, Faculty of Economics, Istanbul University, vol. 16(1), pages 44-54, May.

    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:11:y:2023:i:18:p:3847-:d:1235521. 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.