Continuous Distributions in Engineering and the Applied Sciences: Part I

Description

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, List of Figures List of Tables Preface Glossary of Terms Continuous Random Variables Introduction Continuous Models Standard Distributions Tail Areas Moments and Cumulants Size-Biased Distributions Location-and-Scale Distributions Truncated Distributions Transmuted Distributions Other Extensions Mean Deviation of Continuous Distributions New Measures of Dispersion A New Family of Distributions Random Numbers Data Outliers Summary Rectangular Distribution Introduction Alternate Representations Related Distributions Properties of Rectangular Distribution Moments and Generating Functions Truncated Uniform Distributions Applications Triangular Distributions Summary Exponential Distribution Introduction Alternate Representations Relation to Other Distributions Properties of Exponential Distribution Moments and Generating Functions Additivity Property Memory-Less Property Random Numbers Fitting Generalizations Applications Hydraulics Tensile Strengths Summary Beta Distribution Introduction Alternate Representations Relation to Other Distributions Properties of Type-I Beta Distribution Moments and Generating Functions of Type-I Beta Type-II Beta Distribution Relation to Other Distributions Properties of Type-II Beta Distribution Moments and Generating Functions of Type-II Beta Size-Biased Beta Distributions The Incomplete Beta Function Tail Areas Using IBF Random Numbers Fitting General Beta Distribution Additivity Property Applications Civil Engineering Geotechnical Engineering Beta Distribution in Control Charts Beta Distribution in PERT Confidence Intervals for Binomial Proportions Mineralogy Summary Arcsine Distribution Introduction Alternate Representations Relation to Other Distributions Properties of Arcsine Distribution Moments of Arcsine Distribution Tail Areas Generalized Arcsine Distributions Transmuted Arcsine Distributions Weighted Arcsine Distributions Applications Arcsine Transforms Statistical Physics Random Walks Summary Gamma Distribution Introduction Alternate Representations Relation to Other Distributions Properties of Gamma Distribution Additivity Property Moments and Generating Functions Tail Areas Incomplete Gamma Function (IGF) Fitting General Gamma Distributions Truncated Gamma Distributions Applications Metallurgy Reliability Summary Cosine Distribution Introduction Alternate Representations Properties of Cosine Distribution Mean and Variance Tail Areas Truncated Cosine Distributions Size-Biased Cosine Distribution Transmuted Cosine Distribution Special Cosine Distributions Applications Digital Signal Processing Path Planning in Robotics Antenna Design Summary Normal Distribution Introduction Alternate Representations Relation to Other Distributions Properties of Normal Distribution Moments and Generating Functions Transformations to Normality Tail Areas Additivity Property Special Normal Distributions Truncated Normal Distribution Skew-Normal Distribution Properties of SND The MGF of SND Random Samples Fitting SND Extensions of SND Lognormal Distribution Alternate Representations Properties of Lognormal Distribution Moments Generating Functions Partial Expectation of Lognormal Distribution Fitting Lognormal Distribution Applications Process Control Classification Summary Cauchy Distribution Introduction Alternate Representations Properties of Cauchy Distribution Relation with Other Distributions Functions of Cauchy Variates Parameter Estimation Tail Areas Special Cauchy Distributions Truncated Cauchy Distribution Log-Cauchy Distribution Half-Cauchy Distribution Skew-Cauchy Distribution Beta-Cauchy Distribution Applications Thermodynamics Carbon Nanotube Strain Sensing Biology Summary Bibliography Authors' Biographies Index Blank Page