Exact Saddlepoint Approximations
研究了重归一化鞍点近似对估计量概率密度的精确性，发现只有正态、伽马和逆正态分布能使该近似精确再现样本均值的密度。
The renormalized saddlepoint approximation to the probability density of an estimator often has a surprisingly low relative error over the whole admissible range of the parameter. In particular it is known to be exact for certain densities. This raises the question of how to characterize the class of such exact cases. The density of the mean of a univariate random sample is discussed. It is shown that the normal, gamma and inverse normal are the only possible densities for which the renormalized saddlepoint approximation reproduces exactly the density of the mean.