Continuous Distributions in Engineering and the Applied Sciences -- Part I Synthesis Lectures on Mathematics & Statistics Series

This is an introductory book on continuous statistical distributions and its applications. It is primarily written for graduate students in engineering, undergraduate students in statistics, econometrics, and researchers in various fields. The purpose is to give a self-contained introduction to most commonly used classical continuous distributions in two parts. Important applications of each distribution in various applied fields are explored at the end of each chapter. A brief overview of the chapters is as follows. Chapter 1 discusses important concepts on continuous distributions like location-and-scale distributions, truncated, size-biased, and transmuted distributions. A theorem on finding the mean deviation of continuous distributions, and its applications are also discussed. Chapter 2 is on continuous uniform distribution, which is used in generating random numbers from other distributions. Exponential distribution is discussed in Chapter 3, and its applications briefly mentioned. Chapter 4 discusses both Beta-I and Beta-II distributions and their generalizations, as well as applications in geotechnical engineering, PERT, control charts, etc. The arcsine distribution and its variants are discussed in Chapter 5, along with arcsine transforms and Brownian motion. This is followed by gamma distribution and its applications in civil engineering, metallurgy, and reliability. Chapter 7 is on cosine distribution and its applications in signal processing, antenna design, and robotics path planning. Chapter 8 discusses the normal distribution and its variants like lognormal, and skew-normal distributions. The last chapter of Part I is on Cauchy distribution, its variants and applications in thermodynamics, interferometer design, and carbon-nanotube strain sensing. A new volume (Part II) covers inverse Gaussian, Laplace, Pareto, ????2, T, F, Weibull, Rayleigh, Maxwell, and Gumbel distributions.

List of Figures.- List of Tables.- Preface.- Glossary of Terms.- Continuous Random Variables.- Rectangular Distribution.- Exponential Distribution.- Beta Distribution.- Arcsine Distribution.- Gamma Distribution.- Cosine Distribution.- Normal Distribution.- Cauchy Distribution.- Bibliography.- Authors' Biographies.- Index.

Rajan Chattamvelli is a professor in the School of Advanced Sciences at VIT University, Vellore, Tamil Nadu. He has published more than 22 research articles in international journals of repute and at various conferences. His research interests are in computational statistics, design of algorithms, parallel computing, data mining, machine learning, blockchain, combinatorics, and big data analytics. His prior assignments include Denver Public Health, Colorado; Metromail Corporation, Lincoln, Nebraska; Frederick University, Cyprus; Indian Institute of Management; Periyar Maniammai University, Thanjavur; and Presidency University, Bangalore.Ramalingam Shanmugam is a honorary professor in the school of Health Administration at Texas State University. He is the editor of the journals Advances in Life Sciences, Global Journal of Research and Review, and International Journal of Research in Medical Sciences, and book review editor of the Journal of Statistical Computation and Simulation. He has published more than 200 research articles and 120 conference papers. His areas of research include theoretical and computational statistics, number theory, operations research, biostatistics, decision making, and epidemiology. His prior assignments include University of South Alabama, University of Colorado at Denver, Argonne National Labs, Indian Statistical Institute, and Mississippi State University. He is a fellow of the International Statistical Institute.