Based on the concepts of skewness and kurtosis, the paper points out a kind of method to judge whether the sampling distribution of sample mean can be normally approximated. Besides,the paper also provides the discuss...Based on the concepts of skewness and kurtosis, the paper points out a kind of method to judge whether the sampling distribution of sample mean can be normally approximated. Besides,the paper also provides the discussion of how to make judgement uinder the following conditions:1. Finite population with outlier; 2. Unknown population distribution.展开更多
摘要设X_1,X_2,…为iid.,EX_1=0,0<EX_1~2<∞。中心极限定理指出:均值序列{X_n}大体上是以1/n^(1/2)的速度趋于0。但是,在{X_n}中也存在快于或慢于这个收敛速度的子序列。本文的结果从一个意义上显示:这种子序列的存在对{X_n}的...摘要设X_1,X_2,…为iid.,EX_1=0,0<EX_1~2<∞。中心极限定理指出:均值序列{X_n}大体上是以1/n^(1/2)的速度趋于0。但是,在{X_n}中也存在快于或慢于这个收敛速度的子序列。本文的结果从一个意义上显示:这种子序列的存在对{X_n}的整体影响不大。具体地,若{C_n≥0,n=1,2,…}和{α_n≥0,n=1,2,…}为两个常数列且至少有一个为有界,则sum from n=1 to ∞ C_n(n^(1/2)^(-a_n)<∞与 sum from n=1 to ∞ C_n|_n|a_n<∞ a.s.等价。展开更多
文摘Based on the concepts of skewness and kurtosis, the paper points out a kind of method to judge whether the sampling distribution of sample mean can be normally approximated. Besides,the paper also provides the discussion of how to make judgement uinder the following conditions:1. Finite population with outlier; 2. Unknown population distribution.
文摘摘要设X_1,X_2,…为iid.,EX_1=0,0<EX_1~2<∞。中心极限定理指出:均值序列{X_n}大体上是以1/n^(1/2)的速度趋于0。但是,在{X_n}中也存在快于或慢于这个收敛速度的子序列。本文的结果从一个意义上显示:这种子序列的存在对{X_n}的整体影响不大。具体地,若{C_n≥0,n=1,2,…}和{α_n≥0,n=1,2,…}为两个常数列且至少有一个为有界,则sum from n=1 to ∞ C_n(n^(1/2)^(-a_n)<∞与 sum from n=1 to ∞ C_n|_n|a_n<∞ a.s.等价。
