EMSE Engineering Management and Systems Engineering

Dr. Johan René van Dorp
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Book: Beyond Beta

Published

1. Samuel Kotz and J. R. van Dorp (2004). "Beyond Beta, Other Continuous Families of Distributions with Bounded Support and Applications", World Scientific Press, Singapore.

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.

Software:
R-package for Generalized Trapezoidal distribution, Courtesy of Jeremy Thoms Hetzel (April 25, 2011).

Maximum Likelihood (ML) Estimator for Triangular, TSP, GTSP and UTSP distributions discussed in Chapters 1, 3, 4 and 6. Software requires a text file with input data in the form of an ordered sample. MLE_Calculator.Exe.

Data Files used in the book in conjuction with MLE_Calculator.Exe:
Chapter 1 - Data Table 1_1.txt, Data Table 1_2.txt

Chapter 3 - Beyond Beta Data Equation 3_4.txt

Chapter 6 - Beyond Beta Data Equation 6_46.txt

Excelspreadsheets:
Spreadsheet to plot Triangular, TSP, GTSP amd UTSP distributions:
UTSP Distribution.xls

Spreadsheet with Interest Rate Data used in Chapter 3:
30-Year US Mortgage Interest Rates.xls

Spreadsheet to plot Generalized Trapezoidal Distributions:
Generalized Trapezoidal Distribution.xls

Spreadsheet with Certificate Deposit Rate Data used in Chapter 6:
US Certifice Deposit Rates.xls

Spreadsheet to plot Reflected Generalized Topp Leone (RGTL) Distributions:
RGTL Distribution.xls

Spreadsheet with 2001 US income data and RGTL ML procedure used in Chapter 7:
US 2001 Income Data and MLE RGTL Distributions.xls

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