论文标题
关于广义双曲线和相关分布的模式和中位数的边界
On bounds for the mode and median of the generalized hyperbolic and related distributions
论文作者
论文摘要
除了某些参数值外，不可用的是广义双曲线（GH）分布模式的封闭形式公式。在本文中，我们利用有关修改后的贝塞尔函数及其比率的文献的结果来获得简单但紧密的双面不等式，以使GH分布的模式为一般参数值。作为一种特殊情况，我们针对方差 - γ（VG）分布的模式推断出紧密的双面不等式，并且通过类似的方法，我们还获得了McKay I型分布模式的紧密双面不平等现象。中位数的类似问题更具挑战性，但是我们猜想了VG和McKay I型分布的中位数的一些单调性结果，我们从我们猜测中位数的一些紧张的双面不平等。数值实验支持了这些猜想，也使我们成为GH分布中位数的猜想紧密下限。
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.
