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

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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