The New Odd Log-Logistic Generalized Inverse Gaussian Regression Model

We define a new four-parameter model called the odd log-logistic generalized inverse Gaussian distribution which extends the generalized inverse Gaussian and inverse Gaussian distributions. We obtain some structural properties of the new distribution. We construct an extended regression model based on this distribution with two systematic structures, which can provide more realistic fits to real data than other special regression models. We adopt the method of maximum likelihood to estimate the model parameters. In addition, various simulations are performed for different parameter settings and sample sizes to check the accuracy of the maximum likelihood estimators. We provide a diagnostics analysis based on case-deletion and quantile residuals. Finally, the potentiality of the new regression model to predict price of urban property is illustrated by means of real data.