On bounds for the mode and median of the generalized hyperbolic and related distributions

  title={On bounds for the mode and median of the generalized hyperbolic and related distributions},
  author={Robert E. Gaunt and Milan Merkle},
  journal={Journal of Mathematical Analysis and Applications},

Tables from this paper

Stein factors for variance-gamma approximation in the Wasserstein and Kolmogorov distances

  • Robert E. Gaunt
  • Mathematics, Computer Science
    Journal of Mathematical Analysis and Applications
  • 2022

On closed-form tight bounds and approximations for the median of a gamma distribution

Numerical simulations and asymptotic analyses are used to bound the median, finding bounds of the form 2−1/k(A + Bk), including an upper bound that is tight for low k and a lower bound that are tight for high k.

The basic distributional theory for the product of zero mean correlated normal random variables

The product of two zero mean correlated normal random variables, and more generally the sum of independent copies of such random variables, has received much attention in the statistics literature

Approximate Stochastic Optimal Control for Linear Time Invariant Systems with Heavy-tailed Disturbances

We propose an open loop control scheme for linear time invariant systems perturbed by multivariate 𝑡 disturbances through the use of quantile reformulations. The multivariate 𝑡 disturbance is



A Stein characterisation of the generalized hyperbolic distribution

The generalized hyperbolic (GH) distributions form a five parameter family of probability distributions that includes many standard distributions as special or limiting cases, such as the generalized

The Generalized Hyperbolic Model: Estimation, Financial Derivatives, and Risk Measures

Preface The aim of this dissertation is to describe more realistic models for financial assets based on generalized hyperbolic (GH) distributions and their subclasses. Generalized hyperbolic

Variance-Gamma approximation via Stein's method

Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of

Hyperbolic Processes in Finance

The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures

Statistical analysis of data from the financial markets shows that generalized hyperbolic (GH) distributions allow a more realistic description of asset returns than the classical normal

Generalized Hyperbolic and Inverse Gaussian Distributions: Limiting Cases and Approximation of Processes

In recent years more realistic stochastic models for price movements in financial markets have been developed by replacing the classical Brownian motion by Levy processes. Among these generalized

Moments of the generalized hyperbolic distribution

A recursive method is demonstrated for obtaining moments of the generalized hyperbolic distribution that is readily programmable for numerical evaluation of moments and an alternative derivation of the moments is given.

Some Inequalities for Modified Bessel Functions

We denote by and the Bessel functions of the first and third kinds, respectively. Motivated by the relevance of the function , , in many contexts of applied mathematics and, in particular, in some

A new type of sharp bounds for ratios of modified Bessel functions