Results 221 to 230 of about 3,756 (256)

A Note on the Kurtosis Ordering of the Generalized Secant Hyperbolic Distribution

Communications in Statistics - Theory and Methods, 2007
Two major generalizations of the hyperbolic secant distribution have been proposed in the statistical literature which both introduce an additional parameter that governs the kurtosis of the generalized distribution. The generalized hyperbolic secant (GHS) distribution was introduced by Harkness and Harkness (1968) who considered the pth convolution of
Ingo Klein, Matthias Fischer
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A Review of Generalized Hyperbolic Distributions

Computational Economics, 2023
Xiao Jiang, Saralees Nadarajah, Thomas Hitchen   +2 more
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The Generalized Hyperbolic Skew Student's t-Distribution

Journal of Financial Econometrics, 2006
In this article we argue for a special case of the generalized hyperbolic (GH) family that we denote as the GH skew Student’s t-distribution. This distribution has the important property that one tail has polynomial and the other exponential behavior. Further, it is the only subclass of the GH family of distributions having this property.
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Infinite divisibility of the hyperbolic and generalized inverse Gaussian distributions

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1977
(~'/z)~/2 x~-le --~':~-~+~ (x>0) , (1) 2 K ~ ( ] / ~ ) has the property of infinite divisibility. It follows simply from this that any mixture of the r-dimensional normal distributions Nr(~, X) determined by setting ~ = # + ~ 2 f i A and X=a2A (2) and letting o -2 follow the distribution (1) is infinitely divisible; here #, fl and A are new parameters,
Barndorff-Nielsen, O., Halgreen, Christian   +1 more
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THE GENERALIZED SECANT HYPERBOLIC DISTRIBUTION AND ITS PROPERTIES

Communications in Statistics - Theory and Methods, 2002
The properties of a family of distributions generalizing the secant hyperbolic are developed. This family consists of symmetric distributions, with kurtosis ranging from 1.8 to infinity, and includes the logistic as a special case, the uniform as a limiting case, and closely approximates the normal and Student's t-distributions with corresponding ...
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Classes of skew generalized hyperbolic secant distributions [PDF]

, 2002
A generalization of the hyperbolic secant distribution which allows both for skewness and for leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to allow for skewness.
Fischer, Matthias J., Vaughan, David
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Generalized Hyperbolic Laws as Limit Distributions for Random Sums

Theory of Probability & Its Applications, 2014
A general theorem is proved stating necessary and sufficient conditions for the convergence of the distributions of sums of a random number of independent identically distributed random variables to one-parameter variance-mean mixtures of normal laws. As a corollary, necessary and sufficient conditions for convergence of the distributions of sums of a ...
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Tail Behaviour and Tail Dependence of Generalized Hyperbolic Distributions

2016
Generalized hyperbolic distributions have been well established in finance during the last two decades. However, their application, in particular the computation of distribution functions and quantiles, is numerically demanding. Moreover, they are, in general, not stable under convolution which makes the computation of quantiles in factor models driven
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Applications of a duality between generalized trigonometric and hyperbolic functions

Journal of Mathematical Analysis and Applications, 2021
Shingo Takeuchi
exaly  

Autoregressive processes with generalized hyperbolic innovations

Communications in Statistics Part B: Simulation and Computation, 2020
Mohsen Maleki
exaly