正态分布无偏估计相关的一个极限定理  

A Limit Theorem Related to Unbiased Estimates of Normal Distributions

作　　者：魏昙荣 曾振柄 WEI Tanrong;ZENG Zhenbing(School of Science,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《大学数学》2022年第4期96-99,共4页College Mathematics

基　　金：国家自然科学基金(12071282)。

摘　　要：数理统计学中常利用修偏系数建立某些分布参数的无偏估计.根据正态标准差的渐近无偏估计中的修偏系数,提出了有关该修偏系数一般形式推广的猜想,将证明的猜想归纳得到一个新的定理,并利用该定理证明了该修偏系数的极限、t分布的极限发布为正态分布及Gamma函数的一个等效无限乘积公式.In mathematical statistics,the modified coefficient is often used to establish unbiased estimation of some distribution parameters.According to the modified coefficient used in the asymptotic unbiased estimation of normal standard deviation,conjecture of the general form of the modified coefficient are proposed,then a new theorem are summarized,and by using the theorem,the limit of the modified coefficient,the limit of the t distribution is a normal distribution and and the equivalent definition for Gamma function using an infinite product are proved.

关 键 词：数理统计 GAMMA函数 修偏系数 

分 类 号：O177.5[理学—数学]