IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i4p935-944.html
   My bibliography  Save this article

A new distribution with decreasing, increasing and upside-down bathtub failure rate

Author

Listed:
  • Silva, Rodrigo B.
  • Barreto-Souza, Wagner
  • Cordeiro, Gauss M.

Abstract

The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the so-called generalized exponential geometric distribution is introduced. The new distribution can have a decreasing, increasing and upside-down bathtub failure rate function depending on its parameters. It includes the exponential geometric (Adamidis and Loukas, 1998), the generalized exponential (Gupta and Kundu, 1999) and the extended exponential geometric (Adamidis et al., 2005) distributions as special sub-models. We provide a comprehensive mathematical treatment of the distribution and derive expressions for the moment generating function, characteristic function and rth moment. An expression for Rényi entropy is obtained, and estimation of the stress-strength parameter is discussed. We estimate the parameters by maximum likelihood and obtain the Fisher information matrix. The flexibility of the new model is illustrated in an application to a real data set.

Suggested Citation

  • Silva, Rodrigo B. & Barreto-Souza, Wagner & Cordeiro, Gauss M., 2010. "A new distribution with decreasing, increasing and upside-down bathtub failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 935-944, April.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:935-944
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00376-4
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Barreto-Souza, Wagner & Cribari-Neto, Francisco, 2009. "A generalization of the exponential-Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2493-2500, December.
    2. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    3. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    4. Kus, Coskun, 2007. "A new lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4497-4509, May.
    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. 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.
    2. A. Asgharzadeh & Hassan S. Bakouch & M. Habibi, 2017. "A generalized binomial exponential 2 distribution: modeling and applications to hydrologic events," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2368-2387, October.
    3. Indranil Ghosh & Saralees Nadarajah, 2017. "On some further properties and application of Weibull-R family of distributions," Papers 1711.00171, arXiv.org.
    4. Saralees Nadarajah & Vicente Cancho & Edwin Ortega, 2013. "The geometric exponential Poisson distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 355-380, August.
    5. Cícero R. B. Dias & Gauss M. Cordeiro & Morad Alizadeh & Pedro Rafael Diniz Marinho & Hemílio Fernandes Campos Coêlho, 2016. "Exponentiated Marshall-Olkin family of distributions," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-21, December.
    6. 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.
    7. Liu, Junfeng & Wang, Yi, 2013. "On Crevecoeur’s bathtub-shaped failure rate model," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 645-660.
    8. Indranil Ghosh & Saralees Nadarajah, 2018. "On Some Further Properties and Application of Weibull-R Family of Distributions," Annals of Data Science, Springer, vol. 5(3), pages 387-399, September.
    9. Bakouch, Hassan S. & Ristić, Miroslav M. & Asgharzadeh, A. & Esmaily, L. & Al-Zahrani, Bander M., 2012. "An exponentiated exponential binomial distribution with application," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1067-1081.
    10. Elbatal I., 2013. "The Kumaraswamy Exponentiated Pareto Distribution," Stochastics and Quality Control, De Gruyter, vol. 28(1), pages 1-8, October.
    11. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.
    12. Morais, Alice Lemos & Barreto-Souza, Wagner, 2011. "A compound class of Weibull and power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1410-1425, March.

    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. 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.
    2. Bakouch, Hassan S. & Ristić, Miroslav M. & Asgharzadeh, A. & Esmaily, L. & Al-Zahrani, Bander M., 2012. "An exponentiated exponential binomial distribution with application," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1067-1081.
    3. Feyza Günay & Mehmet Yilmaz, 2018. "Different Parameter Estimation Methods for Exponential Geometric Distribution and Its Applications in Lifetime Data Analysis," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(2), pages 36-43, September.
    4. Bagheri, S.F. & Bahrami Samani, E. & Ganjali, M., 2016. "The generalized modified Weibull power series distribution: Theory and applications," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 136-160.
    5. Rasool Roozegar & G. G. Hamedani & Leila Amiri & Fatemeh Esfandiyari, 2020. "A New Family of Lifetime Distributions: Theory, Application and Characterizations," Annals of Data Science, Springer, vol. 7(1), pages 109-138, March.
    6. Louzada, Francisco & Roman, Mari & Cancho, Vicente G., 2011. "The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2516-2524, August.
    7. Silva, Rodrigo B. & Bourguignon, Marcelo & Dias, Cícero R.B. & Cordeiro, Gauss M., 2013. "The compound class of extended Weibull power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 352-367.
    8. Mahmoudi, Eisa & Jafari, Ali Akbar, 2012. "Generalized exponential–power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4047-4066.
    9. Mahmoudi, Eisa & Sepahdar, Afsaneh, 2013. "Exponentiated Weibull–Poisson distribution: Model, properties and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 76-97.
    10. 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.
    11. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    12. Shovan Chowdhury, 2014. "Compounded Generalized Weibull Distributions - A Unified Approach," Working papers 148, Indian Institute of Management Kozhikode.
    13. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    14. Ausaina Niyomdecha & Patchanok Srisuradetchai, 2023. "Complementary Gamma Zero-Truncated Poisson Distribution and Its Application," Mathematics, MDPI, vol. 11(11), pages 1-13, June.
    15. Saralees Nadarajah & Vicente Cancho & Edwin Ortega, 2013. "The geometric exponential Poisson distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 355-380, August.
    16. Morais, Alice Lemos & Barreto-Souza, Wagner, 2011. "A compound class of Weibull and power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1410-1425, March.
    17. Ruhul Ali Khan & Murari Mitra, 2021. "Estimation issues in the Exponential–Logarithmic model under hybrid censoring," Statistical Papers, Springer, vol. 62(1), pages 419-450, February.
    18. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.
    19. Bobotas, Panayiotis & Koutras, Markos V., 2019. "Distributions of the minimum and the maximum of a random number of random variables," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 57-64.
    20. Jimut Bahan Chakrabarty & Shovan Chowdhury, 2016. "Compounded Inverse Weibull Distributions: Properties, Inference and Applications," Working papers 213, Indian Institute of Management Kozhikode.

    More about this item

    Statistics

    Access and download statistics

    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:eee:csdana:v:54:y:2010:i:4:p:935-944. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.