%0 Journal Article %A ZHANG Yingying %A RONG Tengzhong %A LI Manman %T When the Sum is a Minimal Sufficient Statistics for the Parameter of a Discrete Distribution with Finite Values? %D 2019 %R 10.3969/j.issn.1001-4268.2019.06.005 %J CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS %P 611-620 %V 35 %N 6 %X

We prove three theorems for iid discrete randomvariables taking two values, three values, and k (3\leq k<\infty) valuesby 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\leq k<\infty) 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.

%U http://aps.ecnu.edu.cn/EN/10.3969/j.issn.1001-4268.2019.06.005