Statistical distributions are fundamental to Statistical Science and are a prime indispensable tool for its applications. This monograph is the first to examine an important but somewhat neglected field — univariate continuous distribution on a bounded domain, excluding the beta distribution. It provides an elementary but thorough discussion of "novel" contributions developed in recent years, such as the two-sided power, generalized trapezoidal and generalized Topp and Leone distributions, among others. It discusses a general framework for constructing two-sided distributions and some of its properties. It contains a comprehensive chapter on the triangular distribution as well as a chapter on earlier extensions not emphasized in existing literature. Special attention is given to estimation, in particular, non-standard maximum likelihood procedures. The applications are drawn mainly from the econometric and engineering domains.

Refer to http://www.seas.gwu.edu/~dorpjr/tab4/publications_book.html for data files for the BEYOND BETA book and software programs for the maximum likelihood procedures.

Contents:

• The Triangular Distribution
• Some Early Extensions of the Triangular Distribution
• The Standard Two-Sided Power Distribution
• The Two-Sided Power Distribution
• The Generalized Trapezoidal Distribution
• Uneven Two-Sided Power Distributions
• The Reflected Generalized Topp and Leone Distribution
• A Generalized Framework for Two-Sided Distributions

“... a general framework for constructing two sided distributions is described. It is proposed that these distributions will be useful in risk evaluation problems.”

“Together with the historical notes, this monograph is an interesting piece of work.”

“This monograph is a good starting-point for models for variables whose domain is necessarily bounded and which may require more flexibility than that afforded by the beta distribution.”