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• catalog abstract "Offering comprehensive coverage of modern probability theory (exclusive of continuous time stochastic processes), this unique book functions as both an introduction for graduate statisticians, mathematicians, engineers, and economists and an encyclopedic reference of the subject for professionals in these fields. It assumes only a knowledge of calculus as well as basic real analysis and linear algebra. Throughout Theoretical Probability for Applications the focus is on the practical uses of this increasingly important tool. It develops topics of discrete time probability theory for use in a multitude of applications, including stochastic processes, theoretical statistics, and other disciplines that require a sound foundation in modern probability theory. Principles of measure theory related to the study of probability theory are developed as they are required throughout the book. The book examines most of the basic probability models that involve only a finite or countably infinite number of random variables. Topics in the "Discrete Models" section include Bernoulli trials, random walks, matching, sums of indicators, multinomial trials. Poisson approximations and processes, sampling. Markov chains, and discrete renewal theory. Nondiscrete models discussed include univariate, Beta, sampling, and Dirichlet distributions as well as order statistics. A separate chapter covers aspects of the multivariate normal model. Every treatment is carried out for both random vectors and random variables. Consequently, the book contains complete proofs of the vector case which often differ in detail from those of the scalar case. . Complete with end-of-chapter exercises that provide both a drill of the material presented and an expansion of that same material, explanations of notations used, and a detailed bibliography. Theoretical Probability for Applications is a practical, easy-to-use reference which accommodates the diverse needs of statisticians, mathematicians, economists, engineers, instructors, and students alike.".
• catalog contributor b7774637.
• catalog created "c1994.".
• catalog date "1994".
• catalog date "c1994.".
• catalog dateCopyrighted "c1994.".
• catalog description ". Complete with end-of-chapter exercises that provide both a drill of the material presented and an expansion of that same material, explanations of notations used, and a detailed bibliography. Theoretical Probability for Applications is a practical, easy-to-use reference which accommodates the diverse needs of statisticians, mathematicians, economists, engineers, instructors, and students alike.".
• catalog description "34. Some Univariate Distributions. 35. Change of Variables. 36. Beta Distributions. 37. Sampling Distributions. 38. Dirichlet Distributions. 39. Order Statistics -- pt. IV. Multivariate Normal Models -- 40. Introduction. 41. Representations. 42. Singular and Nonsingular Distributions. 43. Independence. 44. Conditioning. 45. Distributions of [actual symbol not reproducible]. 46. Matrix Theory -- pt. V. Limit Concepts. 47. Convergence with Probability One. 48. Applications to Statistics. 49. Convergence in Probability. 50. Convergence of Distributions. 51. Characteristic Functions. 52. Central Limit Theorem. 53. Limit Laws for Quantities. 54. Limit Laws for Extreme Order Statistics. 55. The L[subscript p] Spaces. 56. Moment Generating Functions. 57. Zero-One Laws. 58. Random Series of Random Variables. 59. Stationary Sequences and the Ergodic Theorem. 60. Large Deviations Principle. 61. Central Limit Theorems for Dependent Random Variables. 62. Absolutely Continuous and Singular Probability Measures.".
• catalog description "A separate chapter covers aspects of the multivariate normal model. Every treatment is carried out for both random vectors and random variables. Consequently, the book contains complete proofs of the vector case which often differ in detail from those of the scalar case.".
• catalog description "App. 1. Facts on Sequences -- App. 2. [lambda] and [pi] Systems -- App. 3. Outer Measures -- App. 4. Construction of Measures -- App. 5. Monotone Functions on R -- App. 6. Dyadic Expansions -- App. 7. Mappings of [0.1] onto R[superscript 4] -- App. 8. The Cantor Set and the Cantor Function -- App. 9. Translates of Integrable Functions -- App. 10. Nonmeasurable Sets -- App. 11. Convex Functions on R -- App. 12. Some Integrals -- App. 13. Some Abelian Formulas -- App. 14. Some Functional Equations -- App. 15. Kronecker's Lemma -- App. 16. A Result from Number Theory -- Table of Tail Probability Under Standard Normal Distribution.".
• catalog description "Includes bibliographical references (p. 882) and index.".
• catalog description "Offering comprehensive coverage of modern probability theory (exclusive of continuous time stochastic processes), this unique book functions as both an introduction for graduate statisticians, mathematicians, engineers, and economists and an encyclopedic reference of the subject for professionals in these fields. It assumes only a knowledge of calculus as well as basic real analysis and linear algebra.".
• catalog description "The book examines most of the basic probability models that involve only a finite or countably infinite number of random variables. Topics in the "Discrete Models" section include Bernoulli trials, random walks, matching, sums of indicators, multinomial trials. Poisson approximations and processes, sampling. Markov chains, and discrete renewal theory. Nondiscrete models discussed include univariate, Beta, sampling, and Dirichlet distributions as well as order statistics.".
• catalog description "Throughout Theoretical Probability for Applications the focus is on the practical uses of this increasingly important tool. It develops topics of discrete time probability theory for use in a multitude of applications, including stochastic processes, theoretical statistics, and other disciplines that require a sound foundation in modern probability theory. Principles of measure theory related to the study of probability theory are developed as they are required throughout the book.".
• catalog extent "xviii, 894 p. :".
• catalog hasFormat "Theoretical probability for applications.".
• catalog identifier "0471632163 (acid-free paper)".
• catalog isFormatOf "Theoretical probability for applications.".
• catalog isPartOf "Wiley series in probability and mathematical statistics. Probability and mathematical statistics".
• catalog issued "1994".
• catalog issued "c1994.".
• catalog language "eng".
• catalog publisher "New York : Wiley & Sons,".
• catalog relation "Theoretical probability for applications.".
• catalog subject "519.2 20".
• catalog subject "Probabilities.".
• catalog subject "Probability Theory.".
• catalog subject "Probability.".
• catalog subject "QA273 .P7825 1994".
• catalog tableOfContents "34. Some Univariate Distributions. 35. Change of Variables. 36. Beta Distributions. 37. Sampling Distributions. 38. Dirichlet Distributions. 39. Order Statistics -- pt. IV. Multivariate Normal Models -- 40. Introduction. 41. Representations. 42. Singular and Nonsingular Distributions. 43. Independence. 44. Conditioning. 45. Distributions of [actual symbol not reproducible]. 46. Matrix Theory -- pt. V. Limit Concepts. 47. Convergence with Probability One. 48. Applications to Statistics. 49. Convergence in Probability. 50. Convergence of Distributions. 51. Characteristic Functions. 52. Central Limit Theorem. 53. Limit Laws for Quantities. 54. Limit Laws for Extreme Order Statistics. 55. The L[subscript p] Spaces. 56. Moment Generating Functions. 57. Zero-One Laws. 58. Random Series of Random Variables. 59. Stationary Sequences and the Ergodic Theorem. 60. Large Deviations Principle. 61. Central Limit Theorems for Dependent Random Variables. 62. Absolutely Continuous and Singular Probability Measures.".
• catalog tableOfContents "App. 1. Facts on Sequences -- App. 2. [lambda] and [pi] Systems -- App. 3. Outer Measures -- App. 4. Construction of Measures -- App. 5. Monotone Functions on R -- App. 6. Dyadic Expansions -- App. 7. Mappings of [0.1] onto R[superscript 4] -- App. 8. The Cantor Set and the Cantor Function -- App. 9. Translates of Integrable Functions -- App. 10. Nonmeasurable Sets -- App. 11. Convex Functions on R -- App. 12. Some Integrals -- App. 13. Some Abelian Formulas -- App. 14. Some Functional Equations -- App. 15. Kronecker's Lemma -- App. 16. A Result from Number Theory -- Table of Tail Probability Under Standard Normal Distribution.".
• catalog title "Theoretical probability for applications / Sidney C. Port.".
• catalog type "text".