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Mathematical statistics

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Engineering --- Probabilities --- Statistical methods

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Mathematical analysis --- Mathematical statistics --- Mathematical physics --- 517.58 --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Distribution (Probability theory) --- Heat --- Hypergeometric functions. --- Transmission. --- Distribution (Probability theory). --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Functions, Special --- Hypergeometric functions --- Fonctions spéciales --- Fonctions hypergéométriques --- Functions, Special. --- Fonctions spéciales --- Fonctions hypergéométriques --- Distribution (théorie des probabilités) --- Statistique mathematique --- Analyse multivariee

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Stochastic processes --- Formes quadratiques --- Forms [Quadratic ] --- Mathematical statistics --- Random variables --- Statistique mathématique --- Stochastische variabelen --- Variables stochastiques --- Vormen [Quadratische ] --- Wiskundige statistiek --- Forms, Quadratic. --- Random variables. --- Mathematical statistics. --- Statistique mathématique --- Variables aléatoires --- Statistique mathematique --- Analyse multivariee

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This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable functions). Illustrative examples, input-output process, optimal recovery of functions and approximations are given; each section lists an ample number of exercises to heighten understanding of the material. Chapter three discusses deterministic/mathematical and optimization models evolving from differential equations, difference equations, algebraic models, power function models, input-output models and pathway models. Fractional integral and derivative models are examined. Chapter four covers non-deterministic/stochastic models. The random walk model, branching process model, birth and death process model, time series models, and regression type models are examined. The fifth chapter covers optimal design. General linear models from a statistical point of view are introduced; the Gauss–Markov theorem, quadratic forms, and generalized inverses of matrices are covered. Pathway, symmetric, and asymmetric models are covered in chapter six, the concepts are illustrated with graphs. .

Mathematics. --- Integral transforms. --- Operational calculus. --- Special functions. --- Mathematical models. --- Mathematical optimization. --- Mathematical Modeling and Industrial Mathematics. --- Optimization. --- Special Functions. --- Integral Transforms, Operational Calculus. --- Functions, special. --- Integral Transforms. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Special functions --- Fractional calculus. --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus --- Operational calculus --- Differential equations --- Electric circuits --- Models, Mathematical