IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v96y2012i3p409-433.html
   My bibliography  Save this article

The McDonald extended distribution: properties and applications

Author

Listed:
  • Gauss Cordeiro
  • Elizabeth Hashimoto
  • Edwin Ortega
  • Marcelino Pascoa

Abstract

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set. Copyright Springer-Verlag 2012

Suggested Citation

  • Gauss Cordeiro & Elizabeth Hashimoto & Edwin Ortega & Marcelino Pascoa, 2012. "The McDonald extended distribution: properties and applications," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 409-433, July.
  • Handle: RePEc:spr:alstar:v:96:y:2012:i:3:p:409-433
    DOI: 10.1007/s10182-011-0180-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10182-011-0180-3
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10182-011-0180-3?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. Nadarajah, Saralees & Gupta, Arjun K., 2007. "A generalized gamma distribution with application to drought data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(1), pages 1-7.
    2. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    3. Saralees Nadarajah, 2011. "The exponentiated exponential distribution: a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 219-251, September.
    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. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    2. Mehrzad Ghorbani & Seyed Fazel Bagheri & Mojtaba Alizadeh, 2017. "A New Family of Distributions: The Additive Modified Weibull Odd Log-logistic-G Poisson Family, Properties and Applications," Annals of Data Science, Springer, vol. 4(2), pages 249-287, June.
    3. 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.
    4. Mahmoud Aldeni & Carl Lee & Felix Famoye, 2017. "Families of distributions arising from the quantile of generalized lambda distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-18, December.
    5. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    6. Abdus Saboor & Muhammad Nauman Khan & Gauss M. Cordeiro & Marcelino A. R. Pascoa & Juliano Bortolini & Shahid Mubeen, 2019. "Modified beta modified-Weibull distribution," Computational Statistics, Springer, vol. 34(1), pages 173-199, March.
    7. Gauss M. Cordeiro & Giovana O. Silva & Edwin M. M. Ortega, 2016. "An extended-G geometric family," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    8. Yaoting Yang & Weizhong Tian & Tingting Tong, 2021. "Generalized Mixtures of Exponential Distribution and Associated Inference," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    9. Zakeia A. Al-saiary & Rana A. Bakoban & Areej A. Al-zahrani, 2019. "Characterizations of the Beta Kumaraswamy Exponential Distribution," Mathematics, MDPI, vol. 8(1), pages 1-12, December.
    10. Wagner Barreto-Souza & Vinícius Diniz Mayrink, 2019. "Semiparametric generalized exponential frailty model for clustered survival data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 679-701, June.
    11. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy, 2020. "On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    12. Yan Zhou & Zhongmin Liang & Binquan Li & Yixin Huang & Kai Wang & Yiming Hu, 2021. "Seamless Integration of Rainfall Spatial Variability and a Conceptual Hydrological Model," Sustainability, MDPI, vol. 13(6), pages 1-16, March.
    13. Zubair Ahmad, 2020. "The Zubair-G Family of Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 7(2), pages 195-208, June.
    14. Elizabeth Hashimoto & Gauss Cordeiro & Edwin Ortega, 2013. "The new Neyman type A beta Weibull model with long-term survivors," Computational Statistics, Springer, vol. 28(3), pages 933-954, June.
    15. Mashail M. AL Sobhi, 2020. "The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    16. Hassan Amal S. & Elshaarawy Rasha S. & Nagy Heba F., 2022. "Parameter estimation of exponentiated exponential distribution under selective ranked set sampling," Statistics in Transition New Series, Polish Statistical Association, vol. 23(4), pages 37-58, December.
    17. Majdah Badr & Muhammad Ijaz, 2021. "The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-20, March.
    18. Hassan S. Bakouch & Abdus Saboor & Muhammad Nauman Khan, 2021. "Modified Beta Linear Exponential Distribution with Hydrologic Applications," Annals of Data Science, Springer, vol. 8(1), pages 131-157, March.
    19. Altemir Silva Braga & Gauss M. Cordeiro & Edwin M. M. Ortega & Giovana O. Silva, 2017. "The Odd Log-Logistic Student t Distribution: Theory and Applications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 615-639, December.
    20. Debasis Kundu, 2022. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 575-595, November.

    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:alstar:v:96:y:2012:i:3:p:409-433. 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.