ABSTRACT
This chapter provides explanation for different types of discrete count data distributions with range {0,1, 2,…} within the Generalized Additive Models for Location Scale, and Shape (GAMLSS) family. It considers explicit GAMLSS family discrete count distributions on { 0, 1, 2, …}. The chapter also considers overdispersed and underdispersed discrete count distributions relative to the Poisson distribution, including mixture distributions and discretized continuous distributions. It considers zero-inflated and zero-adjusted distributions for modeling an excess or shortage of zero values in a response variable. The chapter compares the skewness and kurtosis of the distributions. Overdispersion is usually defined as the extra variation in a count response variable which is not explained by the Poisson distribution.
