Robert E. Gaunt

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20182025

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math.CA2020

Bounds for an integral of the modified Bessel function of the first kind and expressions involving it

Robert E. Gaunt

Simple upper and lower bounds are obtained for the integral $\int_{0}^{x} e^{- γ t} t^{ν} I_{ν} (t) d t$ , $x > 0$ , $ν > - \frac{1}{2}$ , $0 < γ < 1$ . Most of our bounds for this integral…

math.ST2020

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

Robert E. Gaunt, Milan Merkle

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…