学习《概率论与数理统计》应该注意的若干问题(5)——三大分布在数理统计中的地位

Problems Worthy of Attention in Leaming Probability Theory and Mathematical Statistics——Of the Position of the Three Distribution in Mathematical Statistics

三大分布是指x^2分布、t分布、以及F分布,与正态分布一同构成数理统计中的四大分布。由标准正态总体样本的适当组合构成的统计量形成数理统计中的其他三大基础分布。所以,数理统计中总是以正态总体作为研究对象展开。在数理统计中,"总体"、"抽样"、"样本"是三个基本概念,分位点是"小概率事件"发生的临界点,置信区间是参数估计和假设检验的核心计算问题。理解"如果一轮抽样得到的样本统计量观察值掉入小概率事件区间,则有理由拒绝原始假设"的原理,假设检验的学习就变得容易。为此,我们给出了假设检验模版。

The three distributions, the X2 -distribution, t-distribution and F-distribution, together with the normal distribution constitute the four distributions. The other three major basic distributions in mathematical statistics consist of standard normal overall samples. Therefore, the mathematical statistics is always developed on the basis of the research of the normal overall distributions. In the mathematical statistics, overall, sampling, and sample are the three basic concepts; the small probability event is the critical point of point loci; the confidence interval is the core computing problems parameter estimation and hypothesis test. Learning hypothesis test will become easy if we understand the principle that if the observation value of any sampling statistics gets fall into the small probability events, it would reason to refuse interval original hypothesis. Hence, we provide the hypothesis test model.