Parameter estimation of geographically weighted trivariate Weibull regression model

In this study, Geographically Weighted Trivariate Weibull Regression (GWTWR) model and parameter estimation procedure are proposed. GWTWR is trivariate Weibull regression model which all of the regression parameters depend on the geographical location, and parameter estimation is done locally at each location in the study area. The location is expressed as a point coordinate in two-dimensional geographic space (latitude and longitude). The trivariate Weibull regression model (TWR) is the joint probability density function model of trivariate Weibull distribution, which the scale parameters depend on the covariates (independent variables). The TWR model is constructed from the joint survival function of trivariate Weibull distribution proposed by Lee and Wen, which the scale parameters are stated in the regression parameters with identical covariates and non-identical regression parameters. The goal of this study is to estimate the parameters of GWTWR model by using Maximum Likelihood Estimation (MLE) method. The result showed that the maximum likelihood estimator of GWTWR model was not closed form and it can be obtained by using the Newton-Raphson iterative method. To demonstrate the parameter estimation procedure, the proposed model was applied to the continuous nonnegative data on the real data. Based on the application to the real data, GWTWR model was better than global model (TWR).