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Presents a coherent body of theory for the derivation of the sampling distributions of a wide range of test statistics. Emphasis is on the development of practical techniques. A unified treatment of the theory was attempted, e.g., the author sought to relate the derivations for tests on the circle and the two-sample problem to the basic theory for the one-sample problem on the line. The Markovian nature of the sample distribution function is stressed, as it accounts for the elegance of many of the results achieved, as well as the close relation with parts of the theory of stochastic processes.
Book Synopsis Distribution Theory for Tests Based on the Sample Distribution Function by : J. Durbin
Download or read book Distribution Theory for Tests Based on the Sample Distribution Function written by J. Durbin and published by SIAM. This book was released on 1973-01-01 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a coherent body of theory for the derivation of the sampling distributions of a wide range of test statistics. Emphasis is on the development of practical techniques. A unified treatment of the theory was attempted, e.g., the author sought to relate the derivations for tests on the circle and the two-sample problem to the basic theory for the one-sample problem on the line. The Markovian nature of the sample distribution function is stressed, as it accounts for the elegance of many of the results achieved, as well as the close relation with parts of the theory of stochastic processes.
Book Synopsis DISTRIBUTION THEORY FOR TESTS BASED ON THE SAMPLE DISTRIBUTION FUNCTION- BASED ON LECTURES. by : Conference Board of the Mathematical Sciences
Download or read book DISTRIBUTION THEORY FOR TESTS BASED ON THE SAMPLE DISTRIBUTION FUNCTION- BASED ON LECTURES. written by Conference Board of the Mathematical Sciences and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Distribution Free Tests of Independence Based on the Sample Distribution Function by : J. R. Blum
Download or read book Distribution Free Tests of Independence Based on the Sample Distribution Function written by J. R. Blum and published by . This book was released on 1961 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Book Synopsis Distribution Theory and Transform Analysis by : A.H. Zemanian
Download or read book Distribution Theory and Transform Analysis written by A.H. Zemanian and published by Courier Corporation. This book was released on 2011-11-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Book Synopsis Distribution Theory by : Robert A. Barks
Download or read book Distribution Theory written by Robert A. Barks and published by . This book was released on 1972 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Distributions and Their Applications in Physics is the introduction of the Theory of Distributions and their applications in physics. The book contains a discussion of those topics under the Theory of Distributions that are already considered classic, which include local distributions; distributions with compact support; tempered distributions; the distribution theory in relativistic physics; and many others. The book also covers the Normed and Countably-normed Spaces; Test Function Spaces; Distribution Spaces; and the properties and operations involved in distributions. The text is recommended for physicists that wish to be acquainted with distributions and their relevance and applications as part of mathematical and theoretical physics, and for mathematicians who wish to be acquainted with the application of distributions theory for physics.
Book Synopsis Distributions and Their Applications in Physics by : F. Constantinescu
Download or read book Distributions and Their Applications in Physics written by F. Constantinescu and published by Elsevier. This book was released on 2017-07-26 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributions and Their Applications in Physics is the introduction of the Theory of Distributions and their applications in physics. The book contains a discussion of those topics under the Theory of Distributions that are already considered classic, which include local distributions; distributions with compact support; tempered distributions; the distribution theory in relativistic physics; and many others. The book also covers the Normed and Countably-normed Spaces; Test Function Spaces; Distribution Spaces; and the properties and operations involved in distributions. The text is recommended for physicists that wish to be acquainted with distributions and their relevance and applications as part of mathematical and theoretical physics, and for mathematicians who wish to be acquainted with the application of distributions theory for physics.
This monograph is a compilation of research on the inverse Gaussian distribution. It emphasizes the presentation of the statistical properties, methods, and applications of the two-parameter inverse Gaussian family of distribution. It is useful to statisticians and users of statistical distribution.
Book Synopsis The Inverse Gaussian Distribution by : Raj Chhikara
Download or read book The Inverse Gaussian Distribution written by Raj Chhikara and published by CRC Press. This book was released on 1988-09-29 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a compilation of research on the inverse Gaussian distribution. It emphasizes the presentation of the statistical properties, methods, and applications of the two-parameter inverse Gaussian family of distribution. It is useful to statisticians and users of statistical distribution.
Book Synopsis On the Theory of Modified Randomization Tests for Nonparametric Hypotheses by : Jeyaraj Vadiveloo
Download or read book On the Theory of Modified Randomization Tests for Nonparametric Hypotheses written by Jeyaraj Vadiveloo and published by . This book was released on 1977 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Advanced Theory of Statistics: Distribution theory by : Maurice George Kendall
Download or read book The Advanced Theory of Statistics: Distribution theory written by Maurice George Kendall and published by . This book was released on 1968 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Stein (1972, 1986) provides a flexible method for measuring the deviation of any probability distribution from a given distribution, thus effectively giving the upper bound of the approximation error which can be represented as the expectation of a Stein's operator. Hosking (1990, 1992) proposes the concept of L-moment which better summarizes the characteristics of a distribution than conventional moments (C-moments). The purpose of the paper is to propose new tests for conditional parametric distribution functions with weakly dependent and strictly stationary data generating processes (DGP) by constructing a set of the Stein equations as the L-statistics of conceptual ordered sub-samples drawn from the population sample of distribution; hereafter are referred to as the L-moment (GMLM) tests. The limiting distributions of our tests are nonstandard, depending on test criterion functions used in conditional L-statistics restrictions; the covariance kernel in the tests reflects parametric dependence specification. The GMLM tests can resolve the choice of orthogonal polynomials remaining as an identification issue in the GMM tests using the Stein approximation (Bontemps and Meddahi, 2005, 2006) because L-moments are simply the expectations of quantiles which can be linearly combined in order to characterize a distribution function. Thus, our test statistics can be represented as functions of the quantiles of the conditional distribution under the null hypothesis. In the broad context of goodness-of-fit tests based on order statistics, the methodologies developed in the paper differ from existing methods such as tests based on the (weighed) distance between empirical distribution and a parametric distribution under the null or the tests based on likelihood ratio of Zhang (2002) in two respects: 1) our tests are motivated by the L-moment theory and Stein's method; 2) offer more flexibility because we can select an optimal number of L-moments so that the sample size necessary for a test to attain a given level of power is minimal. Finally, we provide some Monte-Carlo simulations for IID data to examine the size, the power and the robustness of the GMLM test and compare with both existing moment-based tests and tests based on order statistics.
Book Synopsis Testing Distributional Assumptions by : Ba M. Chu
Download or read book Testing Distributional Assumptions written by Ba M. Chu and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stein (1972, 1986) provides a flexible method for measuring the deviation of any probability distribution from a given distribution, thus effectively giving the upper bound of the approximation error which can be represented as the expectation of a Stein's operator. Hosking (1990, 1992) proposes the concept of L-moment which better summarizes the characteristics of a distribution than conventional moments (C-moments). The purpose of the paper is to propose new tests for conditional parametric distribution functions with weakly dependent and strictly stationary data generating processes (DGP) by constructing a set of the Stein equations as the L-statistics of conceptual ordered sub-samples drawn from the population sample of distribution; hereafter are referred to as the L-moment (GMLM) tests. The limiting distributions of our tests are nonstandard, depending on test criterion functions used in conditional L-statistics restrictions; the covariance kernel in the tests reflects parametric dependence specification. The GMLM tests can resolve the choice of orthogonal polynomials remaining as an identification issue in the GMM tests using the Stein approximation (Bontemps and Meddahi, 2005, 2006) because L-moments are simply the expectations of quantiles which can be linearly combined in order to characterize a distribution function. Thus, our test statistics can be represented as functions of the quantiles of the conditional distribution under the null hypothesis. In the broad context of goodness-of-fit tests based on order statistics, the methodologies developed in the paper differ from existing methods such as tests based on the (weighed) distance between empirical distribution and a parametric distribution under the null or the tests based on likelihood ratio of Zhang (2002) in two respects: 1) our tests are motivated by the L-moment theory and Stein's method; 2) offer more flexibility because we can select an optimal number of L-moments so that the sample size necessary for a test to attain a given level of power is minimal. Finally, we provide some Monte-Carlo simulations for IID data to examine the size, the power and the robustness of the GMLM test and compare with both existing moment-based tests and tests based on order statistics.
