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Two new defective distributions based on the Marshall–Olkin extension

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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 \(1\), 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.

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Acknowledgments

The authors thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq/Brazil) for financial support during the course of this project. The authors also thank the Associate Editor and the two referees for carefully reading and for comments which greatly improved the paper.

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Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal de São Carlos, São Carlos, SP, Brasil

    Ricardo Rocha & Vera Tomazella

  2. School of Mathematics, University of Manchester, Manchester, UK

    Saralees Nadarajah

  3. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, Brasil

    Francisco Louzada

Authors
  1. Ricardo Rocha
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  2. Saralees Nadarajah
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  3. Vera Tomazella
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  4. Francisco Louzada
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Correspondence to Ricardo Rocha.

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Rocha, R., Nadarajah, S., Tomazella, V. et al. Two new defective distributions based on the Marshall–Olkin extension. Lifetime Data Anal 22, 216–240 (2016). https://doi.org/10.1007/s10985-015-9328-x

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  • DOI: https://doi.org/10.1007/s10985-015-9328-x

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