Penaksiran Parameter dan Pengujian Hipotesis Model Regresi Weibull Univariat

Abstract

In this study, a univariate Weibull regression model is discussed. The Weibull regression is a regression model developed from the Weibull distribution, that is the Weibull distribution depending on the covariates or the regression parameters. The univariate Weibull regression (UWR) model can involve the survival function model and the mean model of the response variable with the scale parameter stated in the terms of the regression parameters. The aim of this study is to estimate the UWR model parameters using the maximum likelihood estimation (MLE) method, and to test the regression parameters. The result shows that the closed form of the maximum likelihood estimator can not be found analytically, and it can be approximed by using the Newton-Raphson iterative method. The regression parameters testing involves simultaneous and partial test. The test statistic for simultaneous test is Wilk's likelihood ratio. Wilk statistic follows Chi-square distribution, which can be derived from the likelihood ratio test (LRT) method. The test statistic for partial test is Wald and it follows standard normal distribution. The alternative test statistik for partial test is squared of Wald statistic, where it follows Chi-square distribution with one degree of freedom.