Two new defective distributions based on the Marshall–Olkin extension

Ricardo Rocha (), Saralees Nadarajah, Vera Tomazella and Francisco Louzada
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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

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2016, vol. 22, issue 2, No 3, 216-240

Abstract: 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.

Keywords: Cure fraction; Defective models; Gompertz distribution; Inverse Gaussian distribution; Marshall–Olkin family; Survival analysis (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10985-015-9328-x

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