Computational Probability Applications

Editors: Andrew G. Glen, Lawrence M. Leemis



Explores the development and use of the modeling and computational capabilities in the Maple-based APPL programing language to solve real and important problems in probability

Highlights the uses of symbolic algebra with probabilistic/stochastic applications in  variety of contexts

Authors are distinguished leaders in the field and development of computational methods for solving problems expressed using probability models

This focuses on the developing field of building probability models with the power of symbolic algebra systems. The book combines the uses of symbolic algebra with probabilistic/stochastic application and highlights the applications in a variety of contexts. The research explored in each chapter is unified by the use of A Probability Programming Language (APPL) to achieve the modeling objectives. APPL, as a research tool, enables a probabilist or statistician the ability to explore new ideas, methods, and models. Furthermore, as an open-source language, it sets the foundation for future algorithms to augment the original code.

Computational Probability Applications is comprised of fifteen chapters, each presenting a specific application of computational probability using the APPL modeling and computer language. The chapter topics include using inverse gamma as a survival distribution, linear approximations of probability density functions, and also moment-ratio diagrams for univariate distributions. These works highlight interesting examples, often done by undergraduate students and graduate students that can serve as templates for future work. In addition, this book should appeal to researchers and practitioners in a range of fields including probability, statistics, engineering, finance, neuroscience, and economics.

Table of contents

Front Matter
Pages i-x

Accurate Estimation with One Order Statistic
Pages 1-13

On the Inverse Gamma as a Survival Distribution
Pages 15-30

Order Statistics in Goodness-of-Fit Testing
Pages 31-39

The “Straightforward” Nature of Arrival Rate Estimation?
Pages 41-50

Survival Distributions Based on the Incomplete Gamma Function Ratio
Pages 51-58

An Inference Methodology for Life Tests with Full Samples or Type II Right Censoring
Pages 59-73

Maximum Likelihood Estimation Using Probability Density Functions of Order Statistics
Pages 75-85

Notes on Rank Statistics
Pages 87-106

Control Chart Constants for Non-normal Sampling
Pages 107-117

Linear Approximations of Probability Density Functions
Pages 119-132

Univariate Probability Distributions
Pages 133-147

Moment-Ratio Diagrams for Univariate Distributions
Pages 149-164

The Distribution of the Kolmogorov–Smirnov, Cramer–von Mises, and Anderson–Darling Test Statistics for Exponential Populations with Estimated Parameters
Pages 165-190

Parametric Model Discrimination for Heavily Censored Survival Data
Pages 191-215

Lower Confidence Bounds for System Reliability from Binary Failure Data Using Bootstrapping
Pages 217-237

Back Matter
Pages 239-256