ABSTRACT
This chapter provides explanation for different types of continuous distributions defined on the interval (0,1). It also provides how to create distributions on (0, 1) using a logit transformation or truncation. The chapter examines situations where a continuous response variable has its range on the interval between zero and one, excluding the endpoints zero and one. Distributions for bounded continuous random variables have a sparse literature, in comparison with those for unbounded variables. The beta distribution has dominated the analysis of bounded continuous response variables, being until fairly recently the only well-known candidate for this range. The beta distribution is also of use as a mixing distribution for bounded parameters in, for example the beta-binomial distribution.
