Some properties of the generalized Gaussian ratio and their applications
Zhen-Hang Yang, Bo-Yan Xi, Shenzhou Zheng · Mathematical Inequalities & Applications · 2020
We are devoted to an integral, asymptotic expansion and Maclaurin series representation for the generalized Gaussian ratio, and find their various related properties such as complete monotonicity and some useful inequalities. As applications, several simple approximations for its inverse function are presented, which may be essential to the estimations for the shape parameter of the generalized Gaussian distribution.