Beyond Beta: Other Continuous Families Of Distributions With Bounded Support And Applications Other Continuous Families of Distributions with Bounded Support and Applications

"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 area in this field - univariate continuous distributions on a bounded domain, excluding the beta distribution. It provides an elementary but thorough discussion of "novel" contributions developed in recent years and some of their applications. It contains a comprehensive chapter on the triangular distribution as well as a chapter on earlier extensions of this distribution not emphasized in existing statistical literature. Special attention is given to estimation, in particular, non-standard maximum likelihood procedures."--BOOK JACKET 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. One of our goals in this book is to "dig out" suitable substitutes of the beta distribution.