Computational Probability: Algorithms and Applications in the Mathematical Sciences

✍ Scribed by John H. Drew, Diane L. Evans, Andrew G. Glen, Lawrence M. Leemis (auth.)

• Publisher: Springer International Publishing
• Year: 2017
• Tongue: English
• Leaves: 336
• Series: International Series in Operations Research & Management Science 246
• Edition: 2
• Category: Library

✦ Synopsis

This new edition includes the latest advances and developments in computational probability involving A Probability Programming Language (APPL). The book examines and presents, in a systematic manner, computational probability methods that encompass data structures and algorithms. The developed techniques address problems that require exact probability calculations, many of which have been considered intractable in the past. The book addresses the plight of the probabilist by providing algorithms to perform calculations associated with random variables.
Computational Probability: Algorithms and Applications in the Mathematical Sciences, 2nd Edition begins with an introductory chapter that contains short examples involving the elementary use of APPL. Chapter 2 reviews the Maple data structures and functions necessary to implement APPL. This is followed by a discussion of the development of the data structures and algorithms (Chapters 3–6 for continuous random variables and Chapters 7–9 for discrete random variables) used in APPL. The book concludes with Chapters 10–15 introducing a sampling of various applications in the mathematical sciences. This book should appeal to researchers in the mathematical sciences with an interest in applied probability and instructors using the book for a special topics course in computational probability taught in a mathematics, statistics, operations research, management science, or industrial engineering department.

✦ Table of Contents

Front Matter....Pages i-xi
Front Matter....Pages 1-1
Computational Probability....Pages 3-11
Maple for APPL....Pages 13-30
Front Matter....Pages 31-31
Data Structures and Simple Algorithms....Pages 33-45
Transformations of Random Variables....Pages 47-56
Bivariate Transformations of Random Variables....Pages 57-72
Products of Random Variables....Pages 73-86
Front Matter....Pages 87-87
Data Structures and Simple Algorithms....Pages 89-109
Sums of Independent Discrete Random Variables....Pages 111-138
Order Statistics for Random Sampling from Discrete Populations....Pages 139-151
Front Matter....Pages 153-153
Reliability and Survival Analysis....Pages 155-190
Symbolic ARMA Model Analysis....Pages 191-208
Stochastic Simulation....Pages 209-240
Transient Queueing Analysis....Pages 241-275
Bayesian Applications....Pages 277-300
Other Applications....Pages 301-321
Back Matter....Pages 323-336

✦ Subjects

Operation Research/Decision Theory;Statistics and Computing/Statistics Programs;Probability Theory and Stochastic Processes