二项分布基于logit变换的近似信仰推断

APPROXIMATE FIDUCIAL INFERENCE FOR BINOMIAL DISTRIBUTIONS BASED ON THE LOGIT TRANSFORMATION

利用调整的logit变换后估计量的渐近正态性对二项分布建立了近似的枢轴方程,并由此得到了二项分布参数的一种近似信仰分布.对一样本和两样本情形的数值结果表明,该近似信仰分布导出的区间估计具有比文献中推荐的区间估计更好的小样本频率性质.

In this paper, an approximate pivotal equation is constructed for a binomial distribution based on asymptotic normality of a modefied-logit-transformed estimator. Then an approximate fiducial distribution of the binomial parameter is obtained. Numerical results for one-sample cases and two-sample cases show that the interval estimators derived by the approximate fiducial distribution have better finite-sample frequentist properties than those suggested in the literature.