Generalized hyperbolic Lévy motions constitute a broad subclass of Lévy processes which are generated by generalized hyperbolic (GH) distributions. GH distributions were introduced in [1] in connection with a project with geologists. The Lebesgue density of this 5-parameter class can be given in the following form dGH(λ,α,β,δ,μ)(x) = a(λ, α, β, δ, μ)(δ + (x− μ)2)(λ− 1 2 )/2 × Kλ− 2 (α √ δ2 + (x...

In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases include Gaussian scale mixtures and Laplace scale mixtures. Furthermore, Laplace s...

The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. The family nests as particular cases several important asymmetric distributions like the Generalised Hyperbolic distribution. The Generalised Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multivariate ...

After generalization of Shannon‘s entropy measure by Renyi in 1961, many generalized versions of Shannon measure were proposed by different authors. Shannon measure can be obtained from these generalized measures asymptotically. A natural question arises in the parametric generalization of Shannon‘s entropy measure. What is the role of the parameter(s) from application point of view? In the pre...

‎the aim of this paper is to study distribution of ratios of generalized order statistics from pareto distribution. parameter estimation of pareto distribution based on generalized order statistics and ratios of them have been obtained. inferences using method of moments and unbiased estimator have been obtained to develop point estimations. consistency of unbiased estimator has been illustrate...