Related papers: The Variance-Gamma Distribution: A Review
The generalized Laplace (GL) distribution, which falls in the larger family of generalized hyperbolic distributions, provides a versatile model to deal with a variety of applications thanks to its shape parameters. The elliptically…
We obtain variance inequalities for quadratic forms of weakly dependent random variables with bounded fourth moments. We also discuss two application. Namely, we use these inequalities for deriving the limiting spectral distribution of a…
The gamma density function is usually defined in interval between zero and infinity. This paper introduces an upper and a lower boundary to this distribution. The parameters which characterize the truncated gamma distribution are evaluated.…
In this paper we introduce two Bayesian estimators for learning the parameters of the Gamma distribution. The first algorithm uses a well known unnormalized conjugate prior for the Gamma shape and the second one uses a non-linear…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
The Gamma-Gamma (GG) distribution has recently attracted the interest within the research community due to its involvement in various communication systems. In the context of RF wireless communications, GG distribution accurately models the…
We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of…
The generalised extreme value (GEV) distribution is a three parameter family that describes the asymptotic behaviour of properly renormalised maxima of a sequence of independent and identically distributed random variables. If the shape…
We obtain new bounds for the solution of the variance-gamma (VG) Stein equation that are of the correct form for approximations in terms of the Wasserstein and Kolmorogorov metrics. These bounds hold for all parameters values of the four…
In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as beta-exponential and generalized Gompertz…
We propose a family of variational approximations to Bayesian posterior distributions, called $\alpha$-VB, with provable statistical guarantees. The standard variational approximation is a special case of $\alpha$-VB with $\alpha=1$. When…
General hypergeometric distribution (GHGD) definition: from a finite space $N$ containing $n$ elements, randomly select totally $T$ subsets $M_i$ (each contains $m_i$ elements, $1 \geq i \geq T$), what is the probability that exactly $x$…
This paper uses convolutions of the gamma density and the one-sided stable density to construct higher level densities. The approach is applied to constructing a 4-parameter Mittag-Leffler density, whose Laplace transform is a corresponding…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…
A new class of distributions, called Generalized One Parameter Polynomial Exponential-G family of distributions is proposed for modelling lifetime data. An account of the structural and reliability properties of the new class is presented.…
This paper investigates Frequentist consistency properties of the posterior distributions constructed via Generalized Variational Inference (GVI). A number of generic and novel strategies are given for proving consistency, relying on the…
The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…
The theory of normal variance mixture distributions is used to provide elementary derivations of closed-form expressions for the definite integrals $\int_0^\infty x^{-2\nu}\cos(bx)\gamma(\nu,\alpha x^2)\,\mathrm{d}x$ (for $\nu>1/2$, $b>0$…
This article provides a general expression for infinitely divisible multivariate gamma distributions defined by their Laplace transforms, as well as the conditional Laplace transform of infinitely divisible multivariate gamma…
The variance gamma model is a widely popular model for option pricing in both academia and industry. In this paper, we provide a new perspective for pricing European style options for the variance gamma model by deriving closed-form…