First hitting time models for the generalized inverse Gaussian distribution

Barndorff–Nielsen, Ole E.; Blæsild, P.; Halgreen, C.

doi:10.1016/0304-4149(78)90036-4

Cited by 72 publications

(41 citation statements)

References 3 publications

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“…We have seen that a small departure from its shape brings a departure from LS and leads naturally to the DSR. In this respect a useful guide to understanding the specificity of grain distributions could be the observation that generalized inverse Gaussian distributions with p = 1/2 correspond (among others) to first-hitting inverse-time PDF's [75]. This might indicate that our smearings distribute inverse times (i.e., masses) between successive events in a renewal process (such as a passage to a new grain).…”

Section: Discussionmentioning

confidence: 99%

Emergence of special and doubly special relativity

Jizba

Scardigli

2012

Phys. Rev. D

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Building on our previous work [Phys. Rev. D82, 085016 (2010)], we show in this paper how a Brownian motion on a short scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. This can be described in terms of polycrystalline vacuum. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. By analyzing the robustness of such a special relativity under small variations in the polycrystalline grain-size distribution we naturally arrive at the notion of doubly-special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is brought to light. Salient issues such as the rôle of gauge fixing in emergent relativity, generalized commutation relations, Hausdorff dimensions of representative path-integral trajectories and a connection with Feynman chessboard model are also discussed.

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Section: Discussionmentioning

confidence: 99%

Emergence of special and doubly special relativity

Jizba

Scardigli

2012

Phys. Rev. D

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“…where Δ is a positive definite × matrix with determinant |Δ| = 1 and setting κ = − Δ , the norming constant is given by was introduced by the same authors a year earlier (Barndorff-Nielsen, Blaesild, & Halgreen, 1978;O. Barndorff-Nielsen & Halgreen, 1977).…”

Section: Generalised Hyperbolic Distributions (Ghd)mentioning

confidence: 99%

Generalised Lambda Distributions by Method of Moments and Maximum Likelihood using the JSE-ASI Returns

Owusu

Korkpoe

2017

AJFA

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The four-parameter generalised lambda distribution provides the flexibility required to describe the key moments of any distribution as compared with the normal distribution which characterises the distribution with only two moments. As markets have increasingly become nervous, the inadequacies of the normal distribution in capturing correctly the tail events and describing fully the entire distribution of market returns have been laid bare. The focus of this paper is to compare the generalised method of moments (GMM) and maximum likelihood essential estimates (MLE) methods as subsets of the GLD for a better fit of JSE All Share Index returns data. We have demonstrated that the appropriate method of the GLD to completely describe the measures of central tendency and dispersion by additionally capturing the risk dimensions of skewness and kurtosis of the return distribution is the Generalised Method of Moments (GMM) with the Kolmogorov-Smirnoff Distance good-of-fit statistics and the quantile-quantile graph. These measures are very important to any investor in the equity markets.

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“…Some of the probabilistic properties of the distribution (2) were investigated in [4], [6], [10], [14], [19], [20]. Sichel [17] used (2) to construct mixtures of Poisson distributions and Barndorff-Nielson [4] used it to obtain the generalized hyperbolic distribution as a mixture of normal distributions.…”

Section: Exp(-ar -Br X )Dt = 2(b/a) A/2 K a (2vab) Jomentioning

confidence: 99%

“…Sichel [17] used (2) to construct mixtures of Poisson distributions and Barndorff-Nielson [4] used it to obtain the generalized hyperbolic distribution as a mixture of normal distributions. Chaudhry and Ahmad [1] derived the model (2) as a solution to a dynamical system in catastrophe theory.…”

Section: Exp(-ar -Br X )Dt = 2(b/a) A/2 K a (2vab) Jomentioning

confidence: 99%