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• W3048367278 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 approach we also obtain tight two-sided inequalities for the mode of the McKay Type I distribution. The analogous problem for the median is more challenging, but we conjecture some monotonicity results for the median of the VG and McKay Type I distributions, from we which we conjecture some tight two-sided inequalities for their medians. Numerical experiments support these conjectures and also lead us to a conjectured tight lower bound for the median of the GH distribution." @default.
• W3048367278 created "2020-08-18" @default.
• W3048367278 creator A5030985225 @default.
• W3048367278 creator A5077276149 @default.
• W3048367278 date "2021-01-01" @default.
• W3048367278 modified "2023-09-30" @default.
• W3048367278 title "On bounds for the mode and median of the generalized hyperbolic and related distributions" @default.
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• W3048367278 doi "https://doi.org/10.1016/j.jmaa.2020.124508" @default.
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