Some estimation and inference considerations for the zero-inflated discrete Weibull distribution

Count data is ubiquitous in applications spanning diverse research fields, such as ecology, economics, and insurance. However, observed count data often includes excess zeros relative to the assumed count distribution; i.e. zero-inflation. The presence of such “structural zeros” can introduce added variation to the data, resulting in a potential source of data over-dispersion. Thus, it is often of interest to explore zero-inflated models that can handle excess zeros and provide an effective of characterization of data dispersion. To this end, we explore the zero-inflated discrete Weibull, which has received limited attention in the literature. Some basic statistical properties of this distribution, including assessment of a dispersion index, are included. We present both maximum likelihood estimation and minimum distance estimation of the zero-inflated discrete Weibull model as well as discuss some inference considerations for the model. Simulation work is included to highlight these facets of our discussion. Finally, we demonstrate the flexibility and competitiveness of this model on a COVID-19 dataset and a fertility dataset.