IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v34y2019i1d10.1007_s00180-018-0822-y.html
   My bibliography  Save this article

Modified beta modified-Weibull distribution

Author

Listed:
  • Abdus Saboor

    (Kohat University of Science and Technology)

  • Muhammad Nauman Khan

    (Kohat University of Science and Technology)

  • Gauss M. Cordeiro

    (Universidade Federal de Pernambuco)

  • Marcelino A. R. Pascoa

    (Universidade Federal de Mato Grosso)

  • Juliano Bortolini

    (Universidade Federal de Mato Grosso)

  • Shahid Mubeen

    (Sargodha University)

Abstract

We introduce a flexible modified beta modified-Weibull model, which can accommodate both monotonic and non-monotonic hazard rates such as a useful long bathtub shaped hazard rate in the middle. Several distributions can be obtained as special cases of the new model. We demonstrate that the new density function is a linear combination of modified-Weibull densities. We obtain the ordinary and central moments, generating function, conditional moments and mean deviations, residual life functions, reliability measures and mean and variance (reversed) residual life. The method of maximum likelihood and a Bayesian procedure are used for estimating the model parameters. We compare the fits of the new distribution and other competitive models to two real data sets. We prove empirically that the new distribution gives the best fit among these distributions based on several goodness-of-fit statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:1:d:10.1007_s00180-018-0822-y
    DOI: 10.1007/s00180-018-0822-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-018-0822-y
    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/s00180-018-0822-y?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. Pundir, Sudesh & Arora, Sangeeta & Jain, Kanchan, 2005. "Bonferroni Curve and the related statistical inference," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 140-150, November.
    2. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    3. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    4. Singla, Neetu & Jain, Kanchan & Kumar Sharma, Suresh, 2012. "The Beta Generalized Weibull distribution: Properties and applications," Reliability Engineering and System Safety, Elsevier, vol. 102(C), pages 5-15.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Abdul Ghaniyyu Abubakari & Claudio Chadli Kandza-Tadi & Edwin Moyo, 2023. "Modified Beta Inverse Flexible Weibull Extension Distribution," Annals of Data Science, Springer, vol. 10(3), pages 589-617, June.

    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. 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.
    2. 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.
    3. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    4. Cordeiro, Gauss M. & Lemonte, Artur J., 2011. "The beta Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 973-982, August.
    5. Ibrahim Elbatal & Francesca Condino & Filippo Domma, 2016. "Reflected Generalized Beta Inverse Weibull Distribution: definition and properties," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 316-340, November.
    6. 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.
    7. 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.
    8. Psarrakos, Georgios & Toomaj, Abdolsaeed & Vliora, Polyxeni, 2024. "A family of variability measures based on the cumulative residual entropy and distortion functions," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 212-222.
    9. Alzaatreh, Ayman & Famoye, Felix & Lee, Carl, 2014. "The gamma-normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 67-80.
    10. 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.
    11. Ziqing Dong & Yves Tillé & Giovanni M. Giorgi & Alessio Guandalini, 2021. "Linearization and variance estimation of the Bonferroni inequality index," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 1008-1029, July.
    12. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-90, November.
    13. 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.
    14. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
    15. Carol Alexander & Jose Maria Sarabia, 2010. "Endogenizing Model Risk to Quantile Estimates," ICMA Centre Discussion Papers in Finance icma-dp2010-07, Henley Business School, University of Reading.
    16. Yaoting Yang & Weizhong Tian & Tingting Tong, 2021. "Generalized Mixtures of Exponential Distribution and Associated Inference," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    17. Jiong Liu & R. A. Serota, 2023. "Rethinking Generalized Beta family of distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-14, February.
    18. Rasool Roozegar & Saralees Nadarajah & Eisa Mahmoudi, 2022. "The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 44-78, May.
    19. Gauss Cordeiro & Cláudio Cristino & Elizabeth Hashimoto & Edwin Ortega, 2013. "The beta generalized Rayleigh distribution with applications to lifetime data," Statistical Papers, Springer, vol. 54(1), pages 133-161, February.
    20. Nicollas S. S. da Costa & Maria do Carmo Soares de Lima & Gauss Moutinho Cordeiro, 2024. "A Bimodal Exponential Regression Model for Analyzing Dengue Fever Case Rates in the Federal District of Brazil," Mathematics, MDPI, vol. 12(21), pages 1-20, 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:spr:compst:v:34:y:2019:i:1:d:10.1007_s00180-018-0822-y. 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.