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

@article{Gaunt2021OnBF,
  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},
  year={2021},
  volume={493},
  pages={124508}
}
Abstract Except for certain parameter values, a closed form formula for the mode of the generalized hyperbolic (GH) distribution is not available. In this paper, we exploit results from the literature on modified Bessel functions and their ratios to obtain simple but tight two-sided inequalities for the mode of the GH distribution for general parameter values. As a special case, we deduce tight two-sided inequalities for the mode of the variance-gamma (VG) distribution, and through a similar… Expand

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