Preface -- Contents -- Chapter 1 The Triangular Distribution -- 1.1 An Historical Overview -- 1.2 Deriving the CDF utilizing a Geometric Argument -- 1.3 Moments of Triangular Distributions -- 1.4 Maximum Likelihood Method for the Threshold Parameter . -- 1.4.1 An illustrative example -- 1.5 Three Parameter Maximum Likelihood Estimation -- 1.5.1 Some details about the functions G(a, b) and (a, b) -- 1.5.2 ML estimation procedure in pseudo Pascal -- 1.6 Solving for a and b using a Lower and Upper Quantile Estimate -- 1.7 Concluding Remarks -- Chapter 2 Some Early Extensions of the Triangular Distribution -- 2.1 The Topp and Leone Distribution -- 2.1.1 Location estimates of Topp and Leone distributions -- 2.1.2 Variance of Topp and Leone distributions -- 2.1.3 Maximum likelihood estimation -- 2.2 The Trapezoidal Distribution -- 2.2.1 Moments of the trapezoidal distribution -- 2.2.2 Inverse cumulative distribution function -- 2.3 A Linear Combination of Uniform Variables -- 2.3.1 Elementary derivation of the cdf of X given by (2.34) -- 2.3.2 Algorithm for evaluating the cdf given by (2.36) -- 2.4 Concluding Remarks -- Chapter 3 The Standard Two-Sided Power Distribution -- 3.1 Introduction: The Leading Example -- 3.2 The Standard Two-Sided Power Distributions -- 3.2.1 Moments -- 3.2.2 Properties of the cdf -- 3.2.3 Quantile properties -- 3.2.4 Some limiting distributions -- 3.2.5 Relative entropy -- 3.3 Maximum Likelihood Method of Estimating Parameters -- 3.3.1 An illustrative example -- 3.4 Method of Moments -- 3.5 Moment Ratio Diagram Comparison with the Beta Family -- 3.6 Musings on STSP and Beta Families and Concluding Remarks -- Chapter 4 The Two-Sided Power Distribution -- 4.1 Introduction: The Four-Parameter TSP Distribution -- 4.2 Four-Parameter Maximum Likelihood Estimation -- 4.2.1 An illustrative example.

4.3 Elicitation Methods for TSP Distributions -- 4.3.1 Indirect elicitation of the shape parameter n -- 4.3.2 The PERT "controversy" via an illustrative example -- 4.3.3 Indirect elicitation of the parameters a, b and n -- 4.4 Concluding Remarks -- Chapter 5 The Generalized Trapezoidal Distribution -- 5.1 Illustrative Example -- 5.2 The Functional Form of the Generalized Trapezoidal Density -- 5.2.1 Construction of the probability density function -- 5.2.2 Mixing behavior of the component density functions -- 5.3 Basic Properties of the Generalized Trapezoidal Distribution -- 5.3.1 Cumulative distribution function -- 5.3.2 Moments -- 5.4 Concluding Remarks -- Chapter 6 Uneven Two-Sided Power Distributions -- 6.1 Motivation -- 6.2 Derivation of UTSP Family by a Single Limiting Operation -- 6.3 Some Properties of the Uneven STSP Distribution -- 6.4 ML Estimation Procedure for USTSP Distributions -- 6.4.1 Mathematical details of the ML estimation procedure -- 6.5 Illustrative Example -- Chapter 7 The Reflected Generalized Topp and Leone Distribution -- 7.1 Introduction -- 7.2 Cumulative Distribution Function and Density Function -- 7.3 Properties of Standard RGTL Distributions -- 7.3.1 Limiting distributions -- 7.3.2 Some stochastic dominance properties -- 7.3.3 Mode analysis of standard RGTL distributions -- 7.3.4 Failure rate function -- 7.3.5 Cumulative moments -- 7.3.6 Inverse cumulative distribution function -- 7.4 Maximum Likelihood Estimation of SRGTL Parameters -- 7.5 Fitting 2001 US Household Income Distribution Data -- Chapter 8 A Generalized Framework for Two-Sided Distributions -- 8.1 Standard Two-Sided Families of Distributions -- 8.2 The Two-Sided (Linear) Slope Distribution -- 8.2.1 Moment estimation for ST-SS distributions -- 8.2.2 Maximum likelihood estimation of ST-SS parameters -- Epilogue.

Appendix A Graphical Overview of Continuous Univariate Families of Distributions possessing a Bounded Domain -- Appendix B The Johnson SB Distribution -- B.1 Motivation and Representation -- B.2 Some Properties of the Johnson SB Family -- B.2.1 Median value -- B.2.2 Mode analysis -- B.2.3 Moments and parameter estimation -- B.2.4 Some thoughts on limiting distributions -- B.3 Concluding Remarks -- Bibliography -- Author Index -- Subject Index.