## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 25, Number 1 (2011), 64-89.

### The log-generalized modified Weibull regression model

Edwin M. M. Ortega, Gauss M. Cordeiro, and Jalmar M. F. Carrasco

#### Abstract

For the first time, we introduce the log-generalized modified Weibull regression model based on the modified Weibull distribution [Carrasco, Ortega and Cordeiro *Comput. Statist. Data Anal.* **53** (2008) 450–462]. This distribution can accommodate increasing, decreasing, bathtub and unimodal shaped hazard functions. A second advantage is that it includes classical distributions reported in lifetime literature as special cases. We also show that the new regression model can be applied to censored data since it represents a parametric family of models that includes as submodels several widely known regression models and therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. In addition, we define martingale and deviance residuals to detect outliers and evaluate the model assumptions. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 25, Number 1 (2011), 64-89.

**Dates**

First available in Project Euclid: 3 December 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1291387774

**Digital Object Identifier**

doi:10.1214/09-BJPS110

**Mathematical Reviews number (MathSciNet)**

MR2746493

**Zentralblatt MATH identifier**

1300.62019

**Keywords**

Censored data generalized modified Weibull distribution log-Weibull regression residual analysis sensitivity analysis survival function

#### Citation

Ortega, Edwin M. M.; Cordeiro, Gauss M.; Carrasco, Jalmar M. F. The log-generalized modified Weibull regression model. Braz. J. Probab. Stat. 25 (2011), no. 1, 64--89. doi:10.1214/09-BJPS110. https://projecteuclid.org/euclid.bjps/1291387774