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J. Risk Financial Manag. 2018, 11(1), 6; https://doi.org/10.3390/jrfm11010006

Negative Binomial Kumaraswamy-G Cure Rate Regression Model

1
Department of Statistics, Federal University of São Carlos, São Carlos, SP 13565-905, Brazil
2
Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, SP 13565-905, Brazil
3
Department of Statistics, Institute of Mathematics and Statistics, Federal University of Bahia, Salvador, BA 40170-115, Brazil
*
Author to whom correspondence should be addressed.
Received: 8 December 2017 / Revised: 15 January 2018 / Accepted: 16 January 2018 / Published: 19 January 2018
(This article belongs to the Special Issue Extreme Values and Financial Risk)
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Abstract

In survival analysis, the presence of elements not susceptible to the event of interest is very common. These elements lead to what is called a fraction cure, cure rate, or even long-term survivors. In this paper, we propose a unified approach using the negative binomial distribution for modeling cure rates under the Kumaraswamy family of distributions. The estimation is made by maximum likelihood. We checked the maximum likelihood asymptotic properties through some simulation setups. Furthermore, we propose an estimation strategy based on the Negative Binomial Kumaraswamy-G generalized linear model. Finally, we illustrate the distributions proposed using a real data set related to health risk. View Full-Text
Keywords: long-term survivors; Kumaraswamy family; survival analysis; negative binomial distribution; generalized linear model long-term survivors; Kumaraswamy family; survival analysis; negative binomial distribution; generalized linear model
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D’Andrea, A.; Rocha, R.; Tomazella, V.; Louzada, F. Negative Binomial Kumaraswamy-G Cure Rate Regression Model. J. Risk Financial Manag. 2018, 11, 6.

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