Parameterizations for Natural Exponential Families with Quadratic Variance Functions
比较了具有二次方差函数的自然指数族的不同参数化方法，根据似然和后验分布接近正态的程度来评估，并给出了达到近似正态所需的样本量建议。
Abstract Parameterizations for natural exponential families (NEF's) with quadratic variance functions (QVF's) are compared according to the nearness to normality of the likelihood and posterior distribution. Nonnormality of the likelihood (posterior) is measured using two criteria. The first is the magnitude of a standardized third derivative of the log-likelihood (logposterior density); the second is a comparison of the probability of particular tail regions under the normalized likelihood (posterior distribution) and under the corresponding normal approximation. A relationship is given that links these two criteria. Sample sizes are recommended for adequate normality in the likelihood for various parameterizations of the NEF-QVF models, and these results are extended to Bayesian models with a conjugate prior.