Parameter Estimation and Hypothesis Testing of Geographically and Temporally Weighted Bivariate Weibull Regression

Abstract

In global regression, there is an assumption in the form of an error from a normally distributed model, so data that is normally distributed is required. But in reality, not all of the tested data meet the normal distribution. One of the theoretical distributions of continuous random variables that is often used is the Weibull distribution, where the Weibull distribution is a distribution that is often used to analyze the reliability of an object. If there are two response variables that are correlated with each other, the appropriate method used is Bivariate Weibull Regression (BWR). Spatial data has been widely used in various research fields. The Geographically Weighted Bivariate Weibull Regression (GWBWR) model is a model in which there are spatial effects, where there is spatial heterogeneity in bivariate regression with the response variable being Weibull distribution. In addition, panel data has also been applied in various cases, where panel data can provide information covering more than one time period. This can lead to a temporal effect. This study develops a model that can handle cases of spatial and temporal heterogeneity simultaneously, namely the Geographically and Temporally Weighted Bivariate Weibull Regression (GTWBWR) model. The parameter estimation in the model uses the Maximum Likelihood Estimation (MLE) method which gives results that are not closed-form, so it is continued with the Berndt-Hall-Hall-Hausman (BHHH) numerical iteration.
 Keywords: parameter estimation, hypothesis testing, GWBWR