Many known distributions are useful in modeling data but often have limited shapes, such as only being right skewed, left skewed, or symmetric. These limitations make it difficult to use these distributions in broader applications, where data may not follow the shape of these models. By generalizing distributions, adding more parameters increases the flexibility of these distributions in most cases. This allows the new generalizations to have a wider range of applications than the original distribution. The aim of this research was to create a new generalization of the continuous Bernoulli (CB) distribution. In achieving this, a new family of unit-interval distributions could be created to model complex data. With this research, we propose a new generalization of the continuous Bernoulli distribution using the T-R{Y} framework, where we define random variables T, R, and Y that follow specified distributions. With this framework we introduce the T-CB{Cauchy} as well as the T-CB {logistic} families of distributions and investigate the properties of these families. We also investigate the properties of members within the families of these distributions, introducing the normal-CB{Cauchy} and the normal-CB {logistic} distributions. The flexibility of the distributions is observed by fitting the models to different data. Using the T-R{Y} framework, two families of generalized continuous Bernoulli distributions are defined. The properties are investigated, as well as the flexibility is observed in model fitting.

Coauthor is Lucas Robenolt. He and I will both be presenting our research. Links to main articles that were used for the research: https://jsdajournal.springeropen.com/articles/10.1186/2195-5832-1-2 , https://link.springer.com/article/10.1007/s40300-013-0007-y , https://doi.org/10.1081/STA- 120003130