ABSTRACT
This chapter provides explanation for how new continuous distributions can be generated, how some of the distributions are interconnected, and families of distributions. It examines how several of the gamlss.dist distributions can be generated. The chapter describes the methods for generating the gamlss.dist distributions. The methods include transformation from a single random variable, transformation from two or more random variables, Azzalini type methods, splicing distributions, mixtures of distributions, truncation distributions, and systems of distributions. An important disadvantage of distributions generated by Azzalini type methods is that their cdf is not explicitly available, but requires numerical integration. However the distributions can be very flexible in modeling skewness and kurtosis.
