Cover of: inverse Gaussian distribution | V. Seshadri

inverse Gaussian distribution

statistical theory and applications
  • 347 Pages
  • 0.90 MB
  • 6294 Downloads
  • English
by
Springer , New York
Inverse Gaussian distribu
StatementV. Seshadri.
SeriesLecture notes in statistics ;, 137, Lecture notes in statistics (Springer-Verlag) ;, v. 137.
Classifications
LC ClassificationsQA276.7 .S472 1999
The Physical Object
Paginationxii, 347 p. :
ID Numbers
Open LibraryOL376647M
ISBN 100387986189
LC Control Number98038589

The Inverse Gaussian Distribution: Theory: Methodology, and Applications (Statistics: A Series of Textbooks and Monographs) 1st Edition by Raj Chhikara (Author) ISBN Cited by: 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 : Springer-Verlag New York.

This book provides a comprehensive and penetrating account of the inverse Gaussian by: This book provides a comprehensive and penetrating account of the inverse Gaussian law. Beginning with an exhaustive historical overview that presents—for the first time—Etienne Halphen's pioneering wartime contributions, the book proceeds to a rigorous exposition of the theory of exponential families, focusing in particular on the inverse Gaussian : $ inverse Gaussian distribution with parameters λand µ.

An inverse Gaussian random variable X with parameters λand µ has probability density function f(x)= inverse Gaussian distribution book λ 2πx3 e −λ(x−µ)2 2xµ2 x >0, for λ>0 and µ >0.

The inverse Gaussian distribution can be used to model the lifetime of an ob-ject. : The Inverse Gaussian Distribution (Lecture Notes in Statistics) (): Seshadri, V.: BooksCited by: 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 5/5(2). The Inverse Gaussian Distribution The Inverse Gaussian Distribution by V. Seshadri. Download it The Inverse Gaussian Distribution books also available in PDF, EPUB, and Mobi Format for read it on your Kindle device, PC, phones or tablets.

This book is written in the hope that it will serve as a companion volume to my first monograph. In 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 : B.

Jorgensen. A characterization of the inverse Gaussian distribution by Khatri () paralleled the usual characterization of the normal distribution by the independence of sample mean and variance, further reflecting this analogy.

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Wasan and his associates (, ) investigated. The inverse Gaussian is a skew ed, two-parameter continuous distribution whose density is sim- ilar to the Gamma distribution with greater skewness and a sharper peak. The distribution de. The normal-inverse Gaussian distribution (NIG)is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the inverse Gaussian distribution.

The NIG distribution was noted by Blaesild in as a subclass of the generalised hyperbolic distribution discovered by Ole Barndorff-Nielsen. Brand new Book. This book begins with a historical survey of `generalized inverse Gaussian laws', in which the wartime contribution of Etienne Halphen is presented for the first inverse Gaussian distribution, its properties, and its implications are set in a wide perspective.

Brand new Book. 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. This book provides a comprehensive and penetrating account of the inverse Gaussian law.

Beginning with an exhaustive historical overview that presents--for the first time--Etienne Halphen's pioneering wartime contributions, the book proceeds to a rigorous exposition of the theory of exponential families, focusing in particular on the inverse Gaussian law.

About this Item: Springer-Verlag New York Inc., United States, Paperback. Condition: New. Language: English. Brand new Book. In 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.

Exponential Distribution Extreme Value Distribution F Distribution Gamma (and Erlang) Distribution Geometric Distribution Hyperexponential Distribution Hypergeometric Distribution Inverse Chi Squared Distribution Inverse Gamma Distribution Inverse Gaussian (or Inverse Normal) Distribution.

Details inverse Gaussian distribution PDF

The normal-inverse Gaussian distribution (NIG) is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the inverse Gaussian distribution.

The NIG distribution was noted by Blaesild in as a subclass of the generalised hyperbolic distribution discovered by Ole Barndorff-Nielsen. 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.

"This book provides a comprehensive and penetrating account of the inverse Gaussian law. Beginning with an exhaustive historical overview that presents--for the first time--Etienne Halphen's pioneering wartime contributions, the book proceeds to a rigorous exposition of the theory of exponential families, focusing in particular on the inverse Gaussian law.

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. On the Inverse Gaussian Distribution Function. Journal of the American Statistical Association: Vol. 63, No.pp.

Statistical Properties of the Generalized Inverse Gaussian Distribution. Authors (view affiliations) Bent Jørgensen; Book. Buy Softcover Book. Learn about institutional subscriptions. Chapters Table of contents (7 Gaussian distribution Likelihood Normal distribution Properties Variance Verallgemeinerte inverse Gaussverteilung.

Description inverse Gaussian distribution FB2

The Inverse Gaussian Distribution. Density function, distribution function, quantile function, random generation, raw moments, limited moments and moment generating function for the Inverse Gaussian distribution with parameters mean and shape.

Click on the article title to read more. This is a video demonstration of how to show that the Inverse Normal (Inverse Gaussian) distribution is a member of the natural exponential family of distrib. For testing the fit of the inverse Gaussian distribution with unknown parameters, the empirical distribution‐function statistic A 2 is studied.

Two procedures are followed in constructing the test statistic; they yield the same asymptotic distribution. In the first procedure the parameters in the distribution function are directly estimated. The Poisson, gamma, and inverse-Gaussian distributions are perhaps less familiar, and so I provide some more detail:5 • The Gaussian distribution with mean μ and variance σ2 has density function p(y)= 1 σ √ 2π exp (y −μ)2 2σ2 () • The binomial distribution for the proportion Y of successes in n independent binary trials.

Multivariate normal inverse Gaussian distribution: parametrization. Let a scalar quantity u i g, termed the mixing component, be inverse Gaussian distributed u i g ∼ I G (δ g ̃, γ g ̃) where in the standard case δ ̃ g = 1 for all g = 1, 2,G. Hence (1) f (u i g) = 1 2 π exp (γ ̃ g) u i g − 3 2 exp (− 1 2 [1 u i g + γ.

The inverse Gaussian distribution is named so because it satisfies the inverse relationship with a normal distribution (Chhikara and Folks, ). It is also characterized as the distribution of the first passage time of a Brownian motion to a wall with a fixed height or as the limiting distribution of certain types of distributions of waiting.

'This book is an important addition to the literature on the inverse Gaussian distribution.'J.L. Folks, Oklahoma State University, International Statistical Institute, Vol. 14, No. 3 - December"This text provides a thorough, predominantly theoretical, overview of the inverse gaussian distribution and should prove indispensable to those who have discovered the value of this distribution.This distribution appears to have been first derived by Erwin Schrödinger in as the time to first passage of a Brownian motion.

The name inverse Gaussian was proposed by Tweedie in Abraham Wald re-derived this distribution in as the limiting form of a sample in a sequential probability ratio test. Maurice Tweedie investigated this distribution in and established some of.

For nearly 60 years, the lognormal distribution has been the most widely used function in the field of atmospheric science for characterizing atmospheric aerosol size distribution.

We verify whether the three-parameter inverse Gaussian distribution (IGD) is a more suitable function than the lognormal distribution for characterizing aerosol size.