**4. Simulation Study**

In this section, we compare the sample skewness coefficient (*ρ*) and the *n*<sup>−</sup>1/2 skewness coefficients evaluated in the true and estimated parameters (*γ*1 and *γ*1, respectively) of the distributions of the MLEs in the Weibull censored model. To draw the data, we consider three values for *σ*: 0.5, 1 and 3; five sample sizes: 20, 30, 40, 60 and 100; three values for the percent of censoring *C*: 10%, 25% and 50%; and two number of regressors *p*: 3 and 5, where we consider two vectors for *β* in each case: (−2, 0.5, 1) and (1, −0.75, 0.5) for *p* = 3 and (−2, 0.5, 1, −0.3, −0.5) and (1, −0.75, 0.5, −1, 0.8) for *p* = 5. For each combination of *σ*, *β*, % of censoring and sample size we considered 20,000 Monte Carlo replicates. Each vector of covariates *xi* considers an intercept term and the *p* − 1 remaining covariates were drawn independently from the standard normal distribution. Values from the Weibull model are drawn considering the inverse transformation method. Therefore, the greater *n* × *C*/100 values were censored at the observed (1 − *C*/100)-th quantile (a type II censoring scheme). For each sample, we considered the jackknife estimator for *σ*, say *<sup>σ</sup>J*. Therefore, the computation of *γ*1 and *γ*1 was performed considering (*β*, *σ*) and (*β* , *<sup>σ</sup>J*), the true and estimated parameters, respectively. Additionally, *ρ* is computed based on the 20,000 (marginal) skewness coefficient for the components of *β* . Table 1 summarizes the case *β* = (−2, 0.5, 1) (with *p* = 3 regressors) and *C* = 10%. The main conclusions are the following:

**Table 1.** The *n*<sup>−</sup>1/2 and sample skewness coefficients of the distributions of the MLEs in the Weibull censored data with *p* = 3 regressors and *β* = (−2, 0.5, <sup>1</sup>).



from (−1.015, 0.740), (−0.529, 0.426), (−0.372, 0.413), (−0.318, 0.320) and (−0.225, 0.243) for *n* = 20, 30, 40, 60 and 100, respectively. This sugges<sup>t</sup> that, as expected, when *n* increases the skewness coefficient of the MLE estimators for the components of *β* will be more symmetric.

Results sugges<sup>t</sup> that, even with a moderate percentage of censored observations and small sample sizes, the distribution of the MLE for the components of *β* in the Weibull censored model are closer to the symmetry. The combinations of *β*, *p* and *C* not seem to affect the results. A simulation study showing this finding was omitted for the sake of brevity.
