*5.1. Smokers Dataset*

This dataset is related to a clinical trial on the effectiveness of triple-combination pharmacotherapy for tobacco dependence treatment conducted by the Cancer Institute of New Jersey and Robert Wood Johnson Foundation. The trial recruited 127 smokers 18 years or older with predefined medical illnesses from the local community. The outcome were the time (in days) to first relapse (return to smoking). The study lasted 182 days (26 weeks). Therefore, the times are subject to a censoring type I (32% of times were censored). We only considered the 113 patients where such observed time was positive (non-zero). Other measures were assigned randomly treatment group with levels combination or patch only (grp), age in years at time of randomization (age) and employment (full-time or non-full-time). We consider that time*i* ∼WE(*<sup>θ</sup>i*; *<sup>σ</sup>*), where log *θi* = *<sup>X</sup>i β*, *β* = (*β*intercept, *β*grp, *β*age, *β*employment) and

$$X\_i^\top = (1, \texttt{grrp}\_{i\prime} \texttt{age}\_{i\prime} \texttt{employment}\_i)$$

We estimated *σJ* = 1.617008 based on the jackknife method, which was used as known in all the computations. Table 2 shows the parameters estimates, their standard errors and the estimated skewness coefficients and Figure 1 shows the estimated density function based on 1000 bootstrap samples for the coefficients related to the covariates grp, age and employment. Note that the estimated skewness for all parameters were closer to zero, suggesting a symmetric distribution for the estimators which is corroborated by the estimated density based on the bootstrap.

**Figure 1.** Estimated density function based on 1000 bootstrap samples and the asymptotic distribution for *β* grp (left panel), *β* age (center panel) and *β* employment (right panel). The red line denotes the estimated parameter.


**Table 2.** Estimates for parameters and skewness coefficient in smokers dataset.

### *5.2. Insulating Fluids Dataset*

This dataset was presented in [11] on insulating fluids and it is related an accelerated test performed in order to determine the relationship between time (in minutes) to breakdown and voltage (in kilovolts). The authors assumed a regression structure based on the Weibull model and a common censoring time at *L* = 200 (type I censoring), i.e., time*i* <sup>∼</sup>WEI(*<sup>θ</sup>i*, *<sup>σ</sup>*), where log *θi* = *<sup>X</sup>i β*, *i* = 1, ... , 76, *<sup>X</sup>i* = (*β*Intercept, *β*log-voltage). We estimated *σJ* = 1.296704 based on the jackknife method, which was used as known. Table 3 shows the estimates, standard errors and estimated skewness coefficient for the MLE estimators and Figure 2 shows the estimated density function for *β* Intercept and *β* log-voltage. Newly, the estimated skewness for both parameters are closer to zero, suggesting a symmetric distribution for the estimators as also sugges<sup>t</sup> the estimated density based on bootstrap.

> **Table 3.** Estimates for parameters and skewness coefficient in insulating fluids dataset.


**Figure 2.** Estimated density function based on 1000 bootstrap samples and the asymptotic distribution for *β* Intercept (left panel) and *β* log-voltage (right panel). The red line denotes the estimated parameter.
