The monograph is devoted to the use of a computer algebra system to solve problems in operations research and probability. The main purpose of the monograph is to provide algorithms to perform calculations associated with univariate random variables. It refers to the cohesion of data structures and algorithms that automate probability calculations as ‘computational probability’. The data structures and algorithms introduced in the monograph have been implemented in a language known as APPL (A probability programming language). The implementation of the algorithms in Maple-based APPL is available without charge for non-commercial use at www.applsoftware.com. APPL is able to perform exact probability calculations for problems that would otherwise be deemed intractable.
The monograph begins with an introductory chapter, where computational probability and Maple for APPL are considered. Corresponded reviews of the Maple data structures and the functions necessary to implement APPL are given. Chapter 2 contains a brief review of Maple syntax, data structures, and programming constructs used to write the procedures that comprise APPL. Only a small portion of the Maple language is considered.
The second part of the monograph, Chapters 3–5, considers continuous random variables. The data structure used for defining a continuous random variable is defined in Chapter 3. Chapters 4 and 5 contain examples of algorithms devised for manipulating continuous random variables. Chapter 4 considers transformations of continuous random variables and Chapter 5 considers products of continuous random variables.
The third part of the monograph, Chapters 6–8, considers discrete random variables. The data structures that are used for defining a discrete random variable are defined in Chapter 6. Chapters 7 and 8 contain examples of algorithms for manipulating discrete random variables. Chapter 7 considers sums of discrete random variables and Chapter 8 considers the distribution of order statistics drawn from discrete distributions.
The fourth part of the monograph, Chapters 9–11, considers applications of APPL in computational probability. Chapter 9 contains applications in reliability and survival analysis problems, including system design, lower confidence bounds on system reliability, and bootstrapping. Chapter 10 contains APPL applications in discrete-event simulation, including random number testing, input modeling, and goodness-of-fit testing. Finally, Chapter 11 contains miscellaneous applications, such as determining the exact distribution of the time to complete a stochastic activity network, probabilistic analysis of Benford’s law, and the generation of values in statistical tables.
The presented monograph will be of interest for all researchers and specialists that are working in the mathematical sciences with focus on the applied probability. It will be very useful for the lecturers, which could use it for the preparation of special topics courses in computational probability taught in a mathematics, statistics, operations research, management science, or industrial engineering department. The intended audience for the presented monograph includes researchers, MS students, PhD students, and advanced practitioners in stochastic operations research, management science, and applied probability.