2 edition of **Statistical properties of the generalized inverse Gaussian distribution** found in the catalog.

Statistical properties of the generalized inverse Gaussian distribution

Bent JГёrgensen

- 215 Want to read
- 24 Currently reading

Published
**1980**
by Dept. of Theoretical Statistics, Institute of Mathematics, University of Aarhus in Aarhus C, Denmark
.

Written in English

- Inverse Gaussian distribution.,
- Probabilities.

**Edition Notes**

Includes bibliographical references (p. R.1-R.5) and index.

Statement | Bent Jørgensen. |

Series | Memoirs / Dept. of Theoretical Statistics, Institute of Mathematics, University of Aarhus -- no. 4, 1980., Memoirs (Aarhus universitet. Afdeling for teoretisk statistik) -- 1980, no. 4. |

The Physical Object | |
---|---|

Pagination | 1 v. (various pagings) : |

ID Numbers | |

Open Library | OL15410470M |

INVERSE GAUSSIAN DISTRIBUTIONS. 1. The same family appears also as a limiting form for the distribution of the final sample size in a special case of Wald's sequential likelihood ratio test [4]. Some properties of this family were studied in a degree thesis [5], where the Brownian motion problem was found to have an important part in the inter-. ABSTRACT. The matrix generalized inverse Gaussian distribution (MGIG) is shown to arise as a conditional distribution of components of a Wishart distribution. In the special scalar case, the characterization refers to members of the class of generalized inverse Gaussian distributions (GIGs) and includes the inverse Gaussian distribution among.

Nielsen (see Barndorﬀ-Nielsenand Halgreen, ) coined the name generalized inverse Gaussian distribu-tion. It is also known as the Sichel distribution, named after Herbert Sichel, who studied its properties. Its statistical properties are discussed by Bent Jørgensen () and Eberlein and von Hammerstein (). Of course μ (-1 / 2, a, b) is the famous inverse Gaussian distribution introduced by Tweedie (). The properties of the GIG distribution and its statistical applications are investigated in a quite number of books and papers (see Jørgensen, ).Cited by: 8.

Several types of multivariate extensions of the inverse Gaussian (IG) distribution and the reciprocal inverse Gaussian (RIG) distribution are proposed. Some of these types are obtained as random‐additive‐effect models by means of well‐known convolution properties of the IG and RIG distributions, and they have one‐dimensional IG or RIG. The Inverse Gaussian Distribution: Theory: Methodology, and Applications (Statistics: A Series of Textbooks and Monographs) 1st Edition by Raj Chhikara (Author) ISBN ISBN Why is ISBN important? ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Cited by:

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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 by: 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.

Statistical Properties of the Generalized Inverse Gaussian Distribution Statistical Properties of the Generalized Inverse Gaussian Distribution. Authors: Jørgensen, Bent *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis.

ebook access is temporary and does not include ownership of the Brand: Springer-Verlag New York. Statistical Properties of the Generalized Inverse Gaussian Distribution Bent Jørgensen (auth.). 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. Statistical Properties of the Generalized Inverse Gaussian Distribution. Authors (view affiliations) Bent Jørgensen; Book.

Citations; k Downloads; Part of the Lecture Notes in Statistics book series (LNS, volume 9) Log in to check access. Buy eBook.

USD Instant download. Open Library is an open, editable library catalog, building towards a web page for every book ever published. Statistical properties of the generalized inverse Gaussian distribution by Bent Jørgensen,Springer-Verlag edition, in EnglishPages: Statistical Properties of the Generalized Inverse Gaussian Distribution 作者: B.

Jorgensen 出版社: Springer 副标题: 出版年: 页数: 定价: GBP 装帧:. 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.

Leptokurtic distributions are normally more peaked than the normal distribution while platykurtic distributions are more ﬂat topped. 1From greek kyrtosis = curvature from kyrt(´os) = curved, arched, round, swelling, bulging. Sometimes, especially in older literature, γ. 2 is called the coeﬃcient of excess.

Computer algorithms are described for simulation of the generalized inverse Gaussian, generalized hyperbolic and hyperbolic distributions. The efficiencies of the algorithms are found. Timing comparisons with the best available algorithms for sampling the gamma distribution show the new algorithms to be acceptably fast.

The extension to sampling multivariate generalized hyperbolic Cited by: The (univariate) generalized hyperbolic distribution (GHD) family was intensively discussed originally by Barndorff-Nielsen (, ) and arose as specific normal mean-variance mixture: Assuming that X follows a normal distribution with random mean μ + Uβ (μ, β ∈ ℝ) and random variance U, where U in turn is assumed to follow a generalized inverse Gaussian (GIG) distribution.

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.

Statistical Properties of the Exponentiated Generalized Inverted Exponential Distribution. Exponentiated Generalized Inverse Gaussian distribution Lemonte and Cordeiro [8], The Exponentiated Section 3 discusses the statistical properties of the proposed model, and then followed by the concluding remarks in.

Introduction The inverse Gaussian distribution has been studied for a long time and its statistical applications are numerous (see Johnson and Kotz (), Folks and Chhikara ()).

In particular, it is a conjugate family of priors for some distributions in the gamma family (see Exercise of Cited by: Oguntunde et al. (a) proposed the transmuted inverse exponential distribution.

The statistical properties of the exponentiated generalized inverted exponential distribution was examined in. On the Distribution of the Two-Sample Cramer-von Mises Criterion Anderson, T.

W., Annals of Mathematical Statistics, ; Statistical Properties of Inverse Gaussian Distributions. II Tweedie, M. K., Annals of Mathematical Statistics, ; A Characterization of the Inverse Gaussian Distribution Khatri, C. G., Annals of Mathematical Cited by: The EGIG model is a versatile model for analysing lifetime data and has one additional parameter, δ, than the GIG model's three parameters [B.

Jorgensen, Statistical Properties of the Generalized Inverse Gaussian Distribution, Springer-Verlag, New York, ]. For the EGIG model, the maximum-likelihood estimation of the four parameters is Cited by: 1.

1 Introduction.- 2 Basic properties.- Moments and cumulants.- 3 Related distributions.- Normal approximations.- Powers and logarithms of generalized inverse Gaussian variates.- Products and quotients of generalized inverse Gaussian variates.- A generalized inverse Gaussian Markov process.- The generalized hyperbolic distribution.- 4 Maximum likelihood estimation.

I: Mathematical and Statistical Properties. Statistical Properties of the Generalized Inverse Gaussian Distribution. Needlework' by Thérèse de Dillmont is a helpful instructional book. Generating Generalized Inverse Gaussian Random Variates Wolfgang Hormann¨ Josef Leydold Abstract The generalized inverse Gaussian distribution has become quite popular in ﬁnan-cial engineering.

The most popular random variate generator is due to Dagpunar (). It is an acceptance-rejection algorithm method based on the Ratio-of-uniforms File Size: KB.In probability theory and statistics, the generalized inverse Gaussian distribution is a three-parameter family of continuous probability distributions with probability density function f = p / 2 2 K p x e − / 2, x > 0, {\displaystyle f={\frac {^{p/2}}{2K_{p}}}x^{}e^{-/2},\qquad x>0,} where Kp is a modified Bessel function of the second kind, a > 0, b > 0 and p a real parameter.

It is used extensively in geostatistics, statistical Mean: E, , [, x, ], =, b, K, p, +, 1, (, a, b,), a, K, p, (, a, b,), {\displaystyle \operatorname {E} [x]={\frac {{\sqrt {b}}\ K_{p+1}({\sqrt {ab}})}{{\sqrt {a}}\ K_{p}({\sqrt {ab}})}}}, E, , [, x, −, 1, ], =, a, K, p, +, 1, (, a, b,), b, K, p, (, a, b,), −, 2, p, b, {\displaystyle \operatorname {E} [x^{-1}]={\frac {{\sqrt {a}}\ K_{p+1}({\sqrt {ab}})}{{\sqrt {b}}\ K_{p}({\sqrt {ab}})}}-{\frac {2p}{b}}}, E, , [, ln, , x, ], =, ln, , b, a, +, ∂, ∂, p, ln, , K, p, (, a, b,), {\displaystyle \operatorname {E} [\ln x]=\ln {\frac {\sqrt {b}}{\sqrt {a}}}+{\frac {\partial }{\partial p}}\ln K_{p}({\sqrt {ab}})}.

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 time.

The inverse Gaussian distribution, its properties, and its implications are set in a wide : V. Seshadri.