摘要
文献［１］证明了若服从正态分布的随机变量列｛Ｘｎ｝依分布收敛于ｒ．ｖ．Ｘ，则Ｘ服从正态分布或退化分布．文献［２］证明了在一定条件下若在上述命题中把正态分布换为Γ布，则命题仍成立．对几种常见的概率分布，本文给出了类似的结论，在证法上，则求助于矩母函数，比求助于特征函数更为初等．
it is known that the limit distribution of a seguence with normally distributedrandom variables is either a normal distribution or a degraded one[1]. In this note, similar propositions are proved for other commonly used distributions, such as rectangular distribution and Poisson distrbution, etc. and deducing with moment generating functions is more elementary than thatof Fourier-stieltijes transformation.
出处
《天津城市建设学院学报》
CAS
1995年第3期33-38,共6页
Journal of Tianjin Institute of Urban Construction
关键词
极限分布
矩母函数
随机变量列
依分布收敛
正态分布
random variables, probability distributions, convergence in distribution, limit distribution, moment generating functions
