ABSTRACT
This chapter provides a definition of a location and scale family. It also provides an explanation of how the GAMLSS family distributions can model skewness and kurtosis. The prediction deviance is appropriate when the sample is large and where the original observations can be split up into more than one component. Distributions generated by univariate transformation often satisfy all the desirable properties, except perhaps the flexibility in modeling skewness and kurtosis. Another important criterion of choosing a distribution is the robustness of the parameter estimation to outliers. Robustness in this context is how the maximum likelihood estimates of the distribution parameters are affected by extreme outlier values in the response variable.
