Poisson分布的特征

CHARACTERISTICS OF THE POISSON DISTRIBUTION

证明了满足EX =DX <∞的具有非退化分布的母体X服从Poisson分布的充要条件是T2 -T1关于T1有常回归 ,其中T1= X =1n∑ni =1Xi,T2 =1n- 1∑ni =1(Xi- X) 2

This paper proved that population X with EX=DX<∞, and nonsingular distribution is Poisson distribution if, and only if, the statistic T 2-T 1 has constant regression on T 1, where T 1==1n∑ni=1X i is sample mean, and T 2=1n-1∑ni=1(X i-) 2 is sample variance.