This is the second part of our book on continuous statistical distributions. It covers inverse-Gaussian, Birnbaum-Saunders, Pareto, Laplace, central (2), , , Weibull, Rayleigh, Maxwell, and extreme value distributions. Important properties of these distribution are documented, and most common practical applications are discussed. This book can be used as a reference material for graduate courses in engineering statistics, mathematical statistics, and econometrics. Professionals and practitioners working in various fields will also find some of the chapters to be useful. Although an extensive literature exists on each of these distributions, we were forced to limit the size of each chapter and the number of references given at the end due to the publishing plan of this book that limits its size. Nevertheless, we gratefully acknowledge the contribution of all those authors whose names have been left out. Some knowledge in introductory algebra and college calculus is assumed throughout the book. Integration is extensively used in several chapters, and many results discussed in Part I (Chapters 1 to 9) of our book are used in this volume. Chapter 10 is on Inverse Gaussian distribution and its extensions. The Birnbaum-Saunders distribution and its extensions along with applications in actuarial sciences is discussed in Chapter 11. Chapter 12 discusses Pareto distribution and its extensions. The Laplace distribution and its applications in navigational errors is discussed in the next chapter. This is followed by central chi-squared distribution and its applications in statistical inference, bioinformatics and genomics. Chapter 15 discusses Student's distribution, its extensions and applications in statistical inference. The distribution and its applications in statistical inference appears next. Chapter 17 is on Weibull distribution and its applications in geology and reliability engineering. Next two chapters are on Rayleigh and Maxwell distributions and its applications in communications, wind energy modeling, kinetic gas theory, nuclear and thermal engineering, and physical chemistry. The last chapter is on Gumbel distribution, its applications in the law of rare exceedances. Suggestions for improvement are welcome. Please send them to [email protected].

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.

This is an introductory book on discrete statistical distributions and its applications. It discusses only those that are widely used in the applications of probability and statistics in everyday life. The purpose is to give a self-contained introduction to classical discrete distributions in statistics. Instead of compiling the important formulas (which are available in many other textbooks), we focus on important applications of each distribution in various applied fields like bioinformatics, genomics, ecology, electronics, epidemiology, management, reliability, etc., making this book an indispensable resource for researchers and practitioners in several scientific fields. Examples are drawn from different fields. An up-to-date reference appears at the end of the book. Chapter 1 introduces the basic concepts on random variables, and gives a simple method to find the mean deviation (MD) of discrete distributions. The Bernoulli and binomial distributions are discussed in detail in Chapter 2. A short chapter on discrete uniform distribution appears next. The next two chapters are on geometric and negative binomial distributions. Chapter 6 discusses the Poisson distribution in-depth, including applications in various fields. Chapter 7 is on hypergeometric distribution. As most textbooks in the market either do not discuss, or contain only brief description of the negative hypergeometric distribution, we have included an entire chapter on it. A short chapter on logarithmic series distribution follows it, in which a theorem to find the kth moment of logarithmic distribution using (k-1)th moment of zero-truncated geometric distribution is presented. The last chapter is on multinomial distribution and its applications. The primary users of this book are professionals and practitioners in various fields of engineering and the applied sciences. It will also be of use to graduate students in statistics, research scholars in science disciplines, and teachers of statistics, biostatistics, biotechnology, education, and psychology.

This book introduces descriptive statistics and covers a broad range of topics of interest to students and researchers in various applied science disciplines. This includes measures of location, spread, skewness, and kurtosis; absolute and relative measures; and classification of spread, skewness, and kurtosis measures, L-moment based measures, van Zwet ordering of kurtosis, and multivariate kurtosis. Several novel topics are discussed including the recursive algorithm for sample variance; simplification of complicated summation expressions; updating formulas for sample geometric, harmonic and weighted means; divide-and-conquer algorithms for sample variance and covariance; L-skewness; spectral kurtosis, etc. A large number of exercises are included in each chapter that are drawn from various engineering fields along with examples that are illustrated using the R programming language. Basic concepts are introduced before moving on to computational aspects.  Some applications in bioinformatics, finance, metallurgy, pharmacokinetics (PK), solid mechanics, and signal processing are briefly discussed. Every analyst who works with numeric data will find the discussion very illuminating and easy to follow.

DATA MINING METHODS, Second Edition discusses both theoretical foundation and practical applications of datamining in a web field including banking, e-commerce, medicine, engineering and management. This book starts byintroducing data and information, basic data type, data category and applications of data mining. The second chapterbriefly reviews data visualization technology and importance in data mining. Fundamentals of probability and statisticsare discussed in chapter 3, and novel algorithm for sample covariants are derived. The next two chapters give an indepthand useful discussion of data warehousing and OLAP. Decision trees are clearly explained and a new tabularmethod for decision tree building is discussed. The chapter on association rules discusses popular algorithms andcompares various algorithms in summary table form. An interesting application of genetic algorithm is introduced inthe next chapter. Foundations of neural networks are built from scratch and the back propagation algorithm is derivedin the appendix. Popular clustering algorithm is discussed in the next chapter. The web mining chapter generalizes thepage rank metric in multiple ways. A geometric derivation of SDM appear next and summary table in table form isgiven. LSI indexing for IRN extension is discussed next. The book ends with a thorough discussion of text miningmetrics and gives latest research directions in text mining.KEY FEATURES:iC* "Application sections" that demonstrate the usefulness of models presented in each chapteriC* Large number of URL links to software on the net using which readers can build various data mining modelson their owniC* Extensive reference section at the end of each chapter, with 300+ research publications citediC* More than 250 exercises (true/false, multiple choice, computer exercises)

STATISTICAL ALGORITHMS integrates up-to-date theoretical and algorithmic aspects of statistics under one roof. Starting with elementary algorithms on mean, median and mode, it thoroughly discusses variance, covariance, correlation, skewness and kurtosis measures, distance metrics, regression models, and variable selection methods. The chapter on matrix algorithms summarises a large number of useful results. Algorithms for the most popular discrete and continuous statistical distributions appear in chapters 9 and 10. Estimation in a missing data setup is numerically exemplified in the chapter on Expectation Maximisation (EM) algorithm. Random number generation and Monte Carlo methods are also discussed. A key feature of the book is the large number of code-snippets and pseudocode of algorithms. No prior knowledge in statistics or mathematics is assumed on the part of the reader, but only basic knowledge in computer program coding in any high-level language. This book is an invaluable resource for undergraduate students, statisticians and applied mathematicians, computer scientists, engineers and professionals working in related fields.

Researchers and Professionals in data mining and related fields should be familiar with different models and standard algorithms in use to have a clear understanding of the concepts involved. "Data Mining Algorithms" provides the reader with unprecedented insights into the working of various algorithms. Several novel algorithms in association rules, decision trees, statistics, information retrieval etc are clearly defined, and thoroughly discussed. The well-known page rank metric used by search engines is extended in multiple ways in chapter 5 to improve the quality of search results. A highly informative discussion of support vector machines appears in chapter 6. Students in data mining, machine learning, soft computing and statistics will find a wealth of useful and reliable information in this unique and indispensable volume. Scientists, engineers, senior undergraduate and graduate students in applied sciences will all find this book to be extremely useful to sharpen their skills, to improve their general knowledge, and to explore the computational aspects of complex models and algorithms presented.