摘要
利用示性函数技术,我们证明了独立同分布离散随机变量取两个值、三个值和k个值(3≤k<∞)的三个定理.在一定的概率条件下,我们证明了当离散随机变量取两个值、三个值和k个值(3≤k<∞)时,和是未知参数的最小充分统计量.对于骰子的例子,一个图显示六个概率均在0到1之间且它们的和为1,并且一个公平的骰子是可能的.
We prove three theorems for iid discrete random variables taking two values,three values,and k(3≤k<∞)values by using the technique of indicator function.Under some specifications of the probabilities,we prove that the sum is a minimal sufficient statistics for the unknown parameter of interest of the discrete random variable taking two values,three values,and k(3≤k<∞)values.For the dice example,a figure shows that the specifications of the six probabilities are between 0 and 1 and sum to 1,and a fair dice is possible.
作者
张应应
荣腾中
李曼曼
ZHANG Yingying;RONG Tengzhong;LI Manman(Department of Statistics and Actuarial Science,College of Mathematics and Statistics,Chongqing University,Chongqing,401331,China)
出处
《应用概率统计》
CSCD
北大核心
2019年第6期611-620,共10页
Chinese Journal of Applied Probability and Statistics
基金
supported by the Fundamental Research Funds for the Central Universities(Grant Nos.2019CDXYST0016
2018CDXYST0024)
the China Scholarship Council(Grant No.201606055028)
the National Natural Science Foundation of China(Grant No.11671060)
the MOE Project of Humanities and Social Sciences on the West and the Border Area(Grant No.14XJC910001)
关键词
独立同分布随机变量之和
最小充分统计量
离散分布
示性函数
骰子
sum of iid random variables
minimal sufficient statistics
discrete distribution
indicator function
dice
