Abstracts Mathematics

Investigaion of the Gamma Hurdle Model for a Single Population Mean

by Alissa Jacobs

A common issue in some statistical inference problems is dealing with a high frequency of zeroes in a sample of data. For many distributions such as the gamma, optimal inference procedures do not allow for zeroes to be present. In practice, however, it is natural to observe real data sets where nonnegative distributions would make sense to model but naturally zeroes will occur. One example of this is in the analysis of cost in insurance claim studies. One common approach to deal with the presence of zeroes is using a hurdle model. Most literary work on hurdle models will focus on modeling the frequency of zeros separate from the nonnegative values. While this approach has some advantages, it doesn’t typically provide an interval estimator for the global population mean of the variable of interest. In this work we developed a Wald interval for the population mean assuming the gamma hurdle model. Using simulation, we investigated our procedure along with traditional interval estimation strategies such as the t-interval and bootstrap techniques and provided some recommendations and insights. Currently, we recommend the bootstrap t-interval overall as it has better coverage properties across all scenarios we considered.