Simultaneous statistical modelling of excess zeros, over/underdispersion, and multimodality with applications in...

We propose zero-inflated statistical models based on the generalized Hermite distribution for simultaneously modelling of excess zeros, over/underdispersion, and multimodality. These new models are parsimonious yet remarkably flexible allowing the covariates to be introduced directly through the mean, dispersion, and zero-inflated parameters. To accommodate the interval inequality constraint for the dispersion parameter, we present a new link function for the covariate-dependent dispersion regression model. We derive score tests for zero inflation in both covariate-free and covariate-dependent models. Both the score test and the likelihood-ratio test are conducted to examine the validity of zero inflation. The score test provides a useful tool when computing the likelihood-ratio statistic proves to be difficult. We analyse several hotel booking cancellation datasets extracted from two recently published real datasets from a resort hotel and a city hotel. These extracted cancellation datasets reveal complex features of excess zeros, over/underdispersion, and multimodality simultaneously making them difficult to analyse with existing approaches. The application of the proposed methods to the cancellation datasets illustrates the usefulness and flexibility of the models.