统计量x_D~2及其概率性质

众所周知,在数据分析的拟合优度检验中,检验一总体是否服从某一有限的离散概率分布时,通过使用英国统计学家K.Pearson所引入的x~2统计量:x~e=sum from i=1 to r(λ_i(n_i/n-p_i)~2)其中λ_i=n/P_i,n_1 … n_λ=n,P_1 … P_r=1.本文分析K.Pearson x~2统计量的构造源渊,指出其弊端,并引入了结构上更合理的检验用统计量x~2_D,研究了它的均值,方差及渐近分布.

Statistic X_D~2 and Its Properties of Probability

It is known that in the test of fitness in data analysis it is a common way touse the statistic X2 =introduced by British statistician K. Pearson. Thispaper, while discssing the origin of forming the statistic above, points out its disadvantage and gives a new statstic XD2 whose constrution is more reasonable than X 7s. The mean, Variance and asymptotic distribution of XD2 are also studied.