Normal And Student S T Distributions And Their Applications
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Normal And Student S T Distributions And Their Applications
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Author : Mohammad Ahsanullah
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-07
Normal And Student S T Distributions And Their Applications written by Mohammad Ahsanullah and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-07 with Mathematics categories.
The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.
Statistical Distributions
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Author : Nick T. Thomopoulos
language : en
Publisher: Springer
Release Date : 2017-10-10
Statistical Distributions written by Nick T. Thomopoulos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-10 with Mathematics categories.
This book gives a description of the group of statistical distributions that have ample application to studies in statistics and probability. Understanding statistical distributions is fundamental for researchers in almost all disciplines. The informed researcher will select the statistical distribution that best fits the data in the study at hand. Some of the distributions are well known to the general researcher and are in use in a wide variety of ways. Other useful distributions are less understood and are not in common use. The book describes when and how to apply each of the distributions in research studies, with a goal to identify the distribution that best applies to the study. The distributions are for continuous, discrete, and bivariate random variables. In most studies, the parameter values are not known a priori, and sample data is needed to estimate parameter values. In other scenarios, no sample data is available, and the researcher seeks some insight that allows the estimate of the parameter values to be gained. This handbook of statistical distributions provides a working knowledge of applying common and uncommon statistical distributions in research studies. These nineteen distributions are: continuous uniform, exponential, Erlang, gamma, beta, Weibull, normal, lognormal, left-truncated normal, right-truncated normal, triangular, discrete uniform, binomial, geometric, Pascal, Poisson, hyper-geometric, bivariate normal, and bivariate lognormal. Some are from continuous data and others are from discrete and bivariate data. This group of statistical distributions has ample application to studies in statistics and probability and practical use in real situations. Additionally, this book explains computing the cumulative probability of each distribution and estimating the parameter values either with sample data or without sample data. Examples are provided throughout to guide the reader. Accuracy in choosing and applying statistical distributions is particularly imperative for anyone who does statistical and probability analysis, including management scientists, market researchers, engineers, mathematicians, physicists, chemists, economists, social science researchers, and students in many disciplines.
Handbook Of Statistical Distributions With Applications
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Author : K. Krishnamoorthy
language : en
Publisher: CRC Press
Release Date : 2016-01-05
Handbook Of Statistical Distributions With Applications written by K. Krishnamoorthy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-05 with Mathematics categories.
Easy-to-Use Reference and Software for Statistical Modeling and TestingHandbook of Statistical Distributions with Applications, Second Edition provides quick access to common and specialized probability distributions for modeling practical problems and performing statistical calculations. Along with many new examples and results, this edition inclu
Multivariate T Distributions And Their Applications
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Author : Samuel Kotz
language : en
Publisher: Cambridge University Press
Release Date : 2004-02-16
Multivariate T Distributions And Their Applications written by Samuel Kotz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-16 with Mathematics categories.
Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.
Theorems On The Prevalence Threshold And The Geometry Of Screening Curves
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Author : Jacques Balayla
language : en
Publisher: Springer Nature
Release Date : 2024-11-09
Theorems On The Prevalence Threshold And The Geometry Of Screening Curves written by Jacques Balayla and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-09 with Medical categories.
In Theorems on the Prevalence Threshold and the Geometry of Screening Curves, the author explores the mathematical underpinnings of screening and diagnostic testing, offering a unique and novel perspective which employs classical differential geometry and Bayesian theory to elucidate critical aspects of clinical decision-making. Taking the reader on a mathematical journey which bridges these seemingly unrelated worlds, the author presents a quantifiable framework on clinical judgement by introducing the “prevalence threshold” – a novel statistical parameter derived from Bayesian principles by means of the study of the geometry of screening curves. As the prevalence threshold demarcates the pretest probability level beyond which additional information ceases to significantly enhance the yield and reliability of a clinical assessment, it may serve as a benchmark for confidence in clinical decision-making. Given the theorems herein described, readers will find comprehensive analyses and insightful explorations of how these geometric concepts apply to real-world diagnostic scenarios, allowing the clinician to navigate clinical care more effectively at both the individual and public health levels.
Multivariate Normal Distribution The Theory And Applications
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Author : Thu Pham-gia
language : en
Publisher: World Scientific
Release Date : 2021-05-05
Multivariate Normal Distribution The Theory And Applications written by Thu Pham-gia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-05 with Business & Economics categories.
This book provides the reader with user-friendly applications of normal distribution. In several variables it is called the multinormal distribution which is often handled using matrices for convenience. The author seeks to make the arguments less abstract and hence, starts with the univariate case and moves progressively toward the vector and matrix cases. The approach used in the book is a gradual one, going from one scalar variable to a vector variable and to a matrix variable. The author presents the unified aspect of normal distribution, as well as addresses several other issues, including random matrix theory in physics. Other well-known applications, such as Herrnstein and Murray's argument that human intelligence is substantially influenced by both inherited and environmental factors, will be discussed in this book. It is a better predictor of many personal dynamics — including financial income, job performance, birth out of wedlock, and involvement in crime — than are an individual's parental socioeconomic status, or education level, and deserve to be mentioned and discussed.
Mathematical Statistics With Applications In R
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Author : Kandethody M. Ramachandran
language : en
Publisher: Elsevier
Release Date : 2014-09-14
Mathematical Statistics With Applications In R written by Kandethody M. Ramachandran and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-14 with Mathematics categories.
Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner.This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students.Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies. - Step-by-step procedure to solve real problems, making the topic more accessible - Exercises blend theory and modern applications - Practical, real-world chapter projects - Provides an optional section in each chapter on using Minitab, SPSS and SAS commands - Wide array of coverage of ANOVA, Nonparametric, MCMC, Bayesian and empirical methods
Introductory Statistics 2e
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Author : Barbara Illowsky
language : en
Publisher:
Release Date : 2023-12-13
Introductory Statistics 2e written by Barbara Illowsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-13 with Mathematics categories.
Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills. This is an adaptation of Introductory Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.
All Of Statistics
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Author : Larry Wasserman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
All Of Statistics written by Larry Wasserman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
The Theory Of Perfect Learning
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Author : Nonvikan Karl-Augustt Alahassa
language : en
Publisher: Nonvikan Karl-Augustt Alahassa
Release Date : 2021-08-17
The Theory Of Perfect Learning written by Nonvikan Karl-Augustt Alahassa and has been published by Nonvikan Karl-Augustt Alahassa this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-17 with Science categories.
The perfect learning exists. We mean a learning model that can be generalized, and moreover, that can always fit perfectly the test data, as well as the training data. We have performed in this thesis many experiments that validate this concept in many ways. The tools are given through the chapters that contain our developments. The classical Multilayer Feedforward model has been re-considered and a novel $N_k$-architecture is proposed to fit any multivariate regression task. This model can easily be augmented to thousands of possible layers without loss of predictive power, and has the potential to overcome our difficulties simultaneously in building a model that has a good fit on the test data, and don't overfit. His hyper-parameters, the learning rate, the batch size, the number of training times (epochs), the size of each layer, the number of hidden layers, all can be chosen experimentally with cross-validation methods. There is a great advantage to build a more powerful model using mixture models properties. They can self-classify many high dimensional data in a few numbers of mixture components. This is also the case of the Shallow Gibbs Network model that we built as a Random Gibbs Network Forest to reach the performance of the Multilayer feedforward Neural Network in a few numbers of parameters, and fewer backpropagation iterations. To make it happens, we propose a novel optimization framework for our Bayesian Shallow Network, called the {Double Backpropagation Scheme} (DBS) that can also fit perfectly the data with appropriate learning rate, and which is convergent and universally applicable to any Bayesian neural network problem. The contribution of this model is broad. First, it integrates all the advantages of the Potts Model, which is a very rich random partitions model, that we have also modified to propose its Complete Shrinkage version using agglomerative clustering techniques. The model takes also an advantage of Gibbs Fields for its weights precision matrix structure, mainly through Markov Random Fields, and even has five (5) variants structures at the end: the Full-Gibbs, the Sparse-Gibbs, the Between layer Sparse Gibbs which is the B-Sparse Gibbs in a short, the Compound Symmetry Gibbs (CS-Gibbs in short), and the Sparse Compound Symmetry Gibbs (Sparse-CS-Gibbs) model. The Full-Gibbs is mainly to remind fully-connected models, and the other structures are useful to show how the model can be reduced in terms of complexity with sparsity and parsimony. All those models have been experimented, and the results arouse interest in those structures, in a sense that different structures help to reach different results in terms of Mean Squared Error (MSE) and Relative Root Mean Squared Error (RRMSE). For the Shallow Gibbs Network model, we have found the perfect learning framework : it is the $(l_1, \boldsymbol{\zeta}, \epsilon_{dbs})-\textbf{DBS}$ configuration, which is a combination of the \emph{Universal Approximation Theorem}, and the DBS optimization, coupled with the (\emph{dist})-Nearest Neighbor-(h)-Taylor Series-Perfect Multivariate Interpolation (\emph{dist}-NN-(h)-TS-PMI) model [which in turn is a combination of the research of the Nearest Neighborhood for a good Train-Test association, the Taylor Approximation Theorem, and finally the Multivariate Interpolation Method]. It indicates that, with an appropriate number $l_1$ of neurons on the hidden layer, an optimal number $\zeta$ of DBS updates, an optimal DBS learnnig rate $\epsilon_{dbs}$, an optimal distance \emph{dist}$_{opt}$ in the research of the nearest neighbor in the training dataset for each test data $x_i^{\mbox{test}}$, an optimal order $h_{opt}$ of the Taylor approximation for the Perfect Multivariate Interpolation (\emph{dist}-NN-(h)-TS-PMI) model once the {\bfseries DBS} has overfitted the training dataset, the train and the test error converge to zero (0). As the Potts Models and many random Partitions are based on a similarity measure, we open the door to find \emph{sufficient} invariants descriptors in any recognition problem for complex objects such as image; using \emph{metric} learning and invariance descriptor tools, to always reach 100\% accuracy. This is also possible with invariant networks that are also universal approximators. Our work closes the gap between the theory and the practice in artificial intelligence, in a sense that it confirms that it is possible to learn with very small error allowed.