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Two new defective distributions based on the Marshall–Olkin extension

Author

Listed:
  • Ricardo Rocha

    (Universidade Federal de São Carlos)

  • Saralees Nadarajah

    (University of Manchester)

  • Vera Tomazella

    (Universidade Federal de São Carlos)

  • Francisco Louzada

    (Universidade de São Paulo)

Abstract

The presence of immune elements (generating a fraction of cure) in survival data is common. These cases are usually modeled by the standard mixture model. Here, we use an alternative approach based on defective distributions. Defective distributions are characterized by having density functions that integrate to values less than $$1$$ 1 , when the domain of their parameters is different from the usual one. We use the Marshall–Olkin class of distributions to generalize two existing defective distributions, therefore generating two new defective distributions. We illustrate the distributions using three real data sets.

Suggested Citation

  • Ricardo Rocha & Saralees Nadarajah & Vera Tomazella & Francisco Louzada, 2016. "Two new defective distributions based on the Marshall–Olkin extension," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(2), pages 216-240, April.
    • Handle: RePEc:spr:lifeda:v:22:y:2016:i:2:d:10.1007_s10985-015-9328-x
    DOI: 10.1007/s10985-015-9328-x
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    References listed on IDEAS

    as
    1. Gauss Cordeiro & Artur Lemonte, 2013. "On the Marshall–Olkin extended Weibull distribution," Statistical Papers, Springer, vol. 54(2), pages 333-353, May.
    2. Jeremy Balka & Anthony Desmond & Paul McNicholas, 2011. "Bayesian and likelihood inference for cure rates based on defective inverse Gaussian regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(1), pages 127-144.
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    Cited by:

    1. Alex Mota & Eder A. Milani & Vinicius F. Calsavara & Vera L. D. Tomazella & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Francisco Louzada, 2021. "Weighted Lindley frailty model: estimation and application to lung cancer data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 561-587, October.
    2. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.

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