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Products of Random Variables explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and number theory. It uses entirely probabilistic arguments in actualizing the potential of the asymptotic theory of products of independent random variab
Covers the basic probability of distributions with an emphasis on applications from the areas of investments, insurance, and engineering. This book is suitable as a text for senior undergraduate and beginning graduate students in mathematics, statistics, actuarial science, finance, or engineering.
The book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering.
Differentiation and integration in the complex plane; The distribution of sums and differences of Random variables; The distribution of products and quotients of Random variables; The distribution of algebraic functions of independent Random variables; The distribution of algebraic functions of independent H-function variables; Analytical model for evaluation of the H-function inversion integral; Approximating the distribution of an algebraic function of independent random variables; Distribution problems in statistics.
Elements of Probability Theory focuses on the basic ideas and methods of the theory of probability. The book first discusses events and probabilities, including the classical meaning of probability, fundamental properties of probabilities, and the primary rule for the multiplication of probabilities. The text also touches on random variables and probability distributions. Topics include discrete and random variables; functions of random variables; and binomial distributions. The selection also discusses the numerical characteristics of probability distributions; limit theorems and estimates of the mean; and the law of large numbers. The text also describes linear correlation, including conditional expectations and their properties, coefficient of correlation, and best linear approximation to the regression function. The book presents tables that show the values of the normal probability integral, Poisson distribution, and values of the normal probability density. The text is a good source of data for readers and students interested in probability theory.
The book presents statistical methods and models that can usefully support the ev- uation of educational services and quality of products. The contributions collected in this book summarize the work of several researchers from the universities of Bologna, Firenze, Napoli and Padova. The contributions are written with a cons- tent notation and a uni?ed view, and concern methodological advances developed mostly with reference to speci?c problems of evaluation using real data sets. The evaluation of educational services, as well as the analysis of judgements and preferences, poses severe methodological challenges because of the presence of one or more of the following aspects: the observational (non experimental) nature of the context, which is associated with the well-known problems of selection bias and presence of nuisance factors; the hierarchical structure of the data, that entails c- related observations and consideration of effects at different levels of the hierarchy and their interactions (multilevel analysis); the multivariate and qualitative nature of the dependent variable, that requires the use of ad hoc statistical methodologies; the presence of non observable factors, e. g. the satisfaction, calling for the use of latent variables models; the simultaneous presence of components of pleasure and components of uncertainty in the explication of the judgments, that asks for the speci?cation and estimation of mixture models. The ?rst part of the book deals with latent variable models.
Businesses consistently work on new projects, products, and workflows to remain competitive and successful in the modern business environment. To remain zealous, businesses must employ the most effective methods and tools in human resources, project management, and overall business plan execution as competitors work to succeed as well. Advanced Methodologies and Technologies in Business Operations and Management provides emerging research on business tools such as employee engagement, payout policies, and financial investing to promote operational success. While highlighting the challenges facing modern organizations, readers will learn how corporate social responsibility and utilizing artificial intelligence improve a company’s culture and management. This book is an ideal resource for executives and managers, researchers, accountants, and financial investors seeking current research on business operations and management.
Noise is a common factor in most real-world optimization problems. Sources of noise can include physical measurement limitations, stochastic simulation models, incomplete sampling of large spaces and human-computer interaction. Evolutionary algorithms are general, nature-inspired heuristics for numerical search and optimization that are frequently observed to be particularly robust with regard to the effects of noise.