Parameter estimation and application of inverse Gaussian regression

Some cases in environmental studies show that the response variable follows an exponential family, for instance, an inverse Gaussian distribution. Suppose that the positive response variable depends on a set of predictors. We can model it using an inverse Gaussian regression. This study uses the parameter estimation of the inverse Gaussian regression using Maximum Likelihood Estimation (MLE). Since the estimate produced by MLE is not linear, convenient numerical methods are required. The numerical methods used are Fisher scoring and Broyden-Fletcher-Goldfarb-Shanno (BFGS). In this study, we applied inverse Gaussian regression to culinary Micro, Small, and Medium Enterprise resilience data (MSMEs) during extraordinary events. This is an alternative, considering the inverse Gaussian has never been applied outside the survival field. This study aims to obtain an inverse Gaussian regression parameter estimator and factors that influence the resilience of culinary MSMEs from the inverse Gaussian regression application. Fisher scoring and BFGS produce almost the same parameter estimation values. Inverse Gaussian regression’s application produces cost and service time that affect the resilience of culinary MSMEs during extraordinary events.