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Author: Bishnu Goswami Publisher: Bishnu Goswami ISBN: Category : Mathematics Languages : en Pages : 116
Book Description
There are five (basic, for more precise uses, there are many more) sense organs and they all collect data. Their organization, analysis and presentation, when combined is called statistics. One of the most important successes of statistics lies in predicting the outcomes of random events, events which have outcomes that are not predetermined. This prediction, in the applied world, is often the sculpting block which is chiseled away into a fine statue with more real-world data.One of such widely used sculpting block is the ‘particular distribution’, also called the Bell or Gaussian curve. This creates a graph which models binomial distributions (such as the outcomes of a coin toss) when the number of ‘turns’ approaches infinity. Although very important in the theoretical foundations of statistics (especially when considered with the central limit theorem), it is widely used in our day-to-day life, albeit in less mathematically precise way. From snap judgments about on whether to trust an astrological prediction (only for believers in astrology), to corporate boardrooms decisions to hire a candidate based upon standardized tests, the curve and the position of the point sought is often used. These Gaussian curves look like a hill and have their “hilliness” quantified in according to the statistical variance and the mean of the underlying set of data, technically with two main assumptions which prohibits infinite variance and mean. Of course, in many cases these means depend on subjectivity, as in the case of astrological predictions, and in other cases they are very objective (when normed diligently with quantitative data). In this book we delve into the interesting manifestations of Gaussian curves in various arenas of day to day life. This book is not for budding statisticians looking for formal treatments or number crunching, however. This book rather aims to show how the means are distributed along both the quantitative and qualitative aspects of our life, and how they deviate, and what that means for the rest of us. A touch of humor is also in the cards, according to our in-house readers!Some of the topics are discussed relatively simply, for the younger readers and some go into a little more detail. In the experience of the author, this makes reading more interesting and can often motivate the readers for further exploration on the related topics.
Author: Bishnu Goswami Publisher: Bishnu Goswami ISBN: Category : Mathematics Languages : en Pages : 116
Book Description
There are five (basic, for more precise uses, there are many more) sense organs and they all collect data. Their organization, analysis and presentation, when combined is called statistics. One of the most important successes of statistics lies in predicting the outcomes of random events, events which have outcomes that are not predetermined. This prediction, in the applied world, is often the sculpting block which is chiseled away into a fine statue with more real-world data.One of such widely used sculpting block is the ‘particular distribution’, also called the Bell or Gaussian curve. This creates a graph which models binomial distributions (such as the outcomes of a coin toss) when the number of ‘turns’ approaches infinity. Although very important in the theoretical foundations of statistics (especially when considered with the central limit theorem), it is widely used in our day-to-day life, albeit in less mathematically precise way. From snap judgments about on whether to trust an astrological prediction (only for believers in astrology), to corporate boardrooms decisions to hire a candidate based upon standardized tests, the curve and the position of the point sought is often used. These Gaussian curves look like a hill and have their “hilliness” quantified in according to the statistical variance and the mean of the underlying set of data, technically with two main assumptions which prohibits infinite variance and mean. Of course, in many cases these means depend on subjectivity, as in the case of astrological predictions, and in other cases they are very objective (when normed diligently with quantitative data). In this book we delve into the interesting manifestations of Gaussian curves in various arenas of day to day life. This book is not for budding statisticians looking for formal treatments or number crunching, however. This book rather aims to show how the means are distributed along both the quantitative and qualitative aspects of our life, and how they deviate, and what that means for the rest of us. A touch of humor is also in the cards, according to our in-house readers!Some of the topics are discussed relatively simply, for the younger readers and some go into a little more detail. In the experience of the author, this makes reading more interesting and can often motivate the readers for further exploration on the related topics.
Author: Raj Chhikara Publisher: CRC Press ISBN: 9780824779979 Category : Mathematics Languages : en Pages : 232
Book Description
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.
Author: B. Jorgensen Publisher: Springer Science & Business Media ISBN: 1461256984 Category : Mathematics Languages : en Pages : 197
Book Description
In 1978 the idea of studying the generalized inverse Gaussian distribution was proposed to me by Professor Ole Barndorff-Nielsen, who had come across the distribution in the study of the socalled hyperbolic distributions where it emerged in connection with the representation of the hyperbolic distributions as mixtures of normal distributions. The statistical properties of the generalized inverse Gaussian distribution were at that time virtually unde veloped, but it turned out that the distribution has some nice properties, and models many sets of data satisfactorily. This work contains an account of the statistical properties of the distribu tion as far as they are developed at present. The work was done at the Department of Theoretical Statistics, Aarhus University, mostly in 1979, and was partial fulfilment to wards my M. Sc. degree. I wish to convey my warm thanks to Ole Barn dorff-Nielsen and Preben BI~sild for their advice and for comments on earlier versions of the manuscript and to Jette Hamborg for her skilful typing.
Author: Carl Edward Rasmussen Publisher: MIT Press ISBN: 026218253X Category : Computers Languages : en Pages : 266
Book Description
A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
Author: Marvin K. Simon Publisher: Springer Science & Business Media ISBN: 0387476946 Category : Mathematics Languages : en Pages : 218
Book Description
This handbook, now available in paperback, brings together a comprehensive collection of mathematical material in one location. It also offers a variety of new results interpreted in a form that is particularly useful to engineers, scientists, and applied mathematicians. The handbook is not specific to fixed research areas, but rather it has a generic flavor that can be applied by anyone working with probabilistic and stochastic analysis and modeling. Classic results are presented in their final form without derivation or discussion, allowing for much material to be condensed into one volume.
Author: Wlodzimierz Bryc Publisher: Springer Science & Business Media ISBN: 1461225604 Category : Mathematics Languages : en Pages : 142
Book Description
This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3.
Author: V. Seshadri Publisher: Springer Science & Business Media ISBN: 1461214564 Category : Mathematics Languages : en Pages : 363
Book Description
This book is written in the hope that it will serve as a companion volume to my first monograph. The first monograph was largely devoted to the probabilistic aspects of the inverse Gaussian law and therefore ignored the statistical issues and related data analyses. Ever since the appearance of the book by Chhikara and Folks, a considerable number of publications in both theory and applications of the inverse Gaussian law have emerged thereby justifying the need for a comprehensive treatment of the issues involved. This book is divided into two sections and fills up the gap updating the material found in the book of Chhikara and Folks. Part I contains seven chapters and covers distribution theory, estimation, significance tests, goodness-of-fit, sequential analysis and compound laws and mixtures. The first part forms the backbone of the theory and wherever possible I have provided illustrative examples for easy assimilation of the theory. The second part is devoted to a wide range of applications from various disciplines. The applied statistician will find numerous instances of examples which pertain to a first passage time situation. It is indeed remarkable that in the fields of life testing, ecology, entomology, health sciences, traffic intensity and management science the inverse Gaussian law plays a dominant role. Real life examples from actuarial science and ecology came to my attention after this project was completed and I found it impossible to include them.
Author: Eric Jondeau Publisher: Springer Science & Business Media ISBN: 1846286964 Category : Mathematics Languages : en Pages : 541
Book Description
This book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.
Author: M.A. Lifshits Publisher: Springer Science & Business Media ISBN: 9401584745 Category : Mathematics Languages : en Pages : 347
Book Description
It is well known that the normal distribution is the most pleasant, one can even say, an exemplary object in the probability theory. It combines almost all conceivable nice properties that a distribution may ever have: symmetry, stability, indecomposability, a regular tail behavior, etc. Gaussian measures (the distributions of Gaussian random functions), as infinite-dimensional analogues of tht
Author: Bishnu Goswami
Author: Bishnu Goswami
Author: Raj Chhikara
Author: Kenneth S. Miller
Author: B. Jorgensen
Author: Carl Edward Rasmussen
Author: Marvin K. Simon
Author: Wlodzimierz Bryc
Author: V. Seshadri
Author: Eric Jondeau
Author: M.A. Lifshits