Multivariate Weibull regression model

In this study, a multivariate Weibull regression (MWR) model is proposed. The MWR model is a regression model developed from a multivariate Weibull distribution. The proposed MWR model is derived from the joint survival function of the multivariate Weibull distribution developed by Lee and Wen [5], in which the scale parameters are stated in terms of the regression parameters. The aim of this study is to estimate the MWR model parameters using the maximum likelihood estimation (MLE) method, and to test the regression parameters. The results show that the maximum likelihood estimator can be obtained by using the Newton-Raphson iterative method. The regression parameter testing involves simultaneous and partial tests. The test statistic for simultaneous test is Wilk’s likelihood ratio statistic and the test statistic for partial test is Wald statistic. Wilk statistic follows chi-square distribution, which can be derived from the likelihood ratio test (LRT) method. The Wald statistic follows standard normal distribution derived from the asymptotic property of the maximum likelihood estimator.