Abstract
In this paper, we obtain a matrix formula of order n − 1 / 2 , where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.
Highlights
In its first appearance, the Weibull distribution [1] claimed its wide applicability
It is often desirable to test if there are regression parameters statistically significant and the Wald test is commonly performed
The Wald test must be avoided if the sample size is not large enough, because the distribution of the maximum likelihood estimators (MLE) will be poorly approximated by the normal distribution
Summary
The Weibull distribution [1] claimed its wide applicability. There is not a closed-form for the skewness coefficient of γ of the MLE in several regression models. [5] defined the γ1 for the varying dispersion beta regression model and showed that this coefficient for the distribution of the MLE of the precision parameter is relatively large in small to moderate sample sizes. We derive the γ1 coefficient of the distribution of the MLE of the linear parameters in the Weibull censored data, assuming σ known, as σ = 1/2 and 1, the Rayleigh and exponential models, respectively.
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