双截尾柯西分布顺序统计量的概率性质

Probability Properties of Order Statistics to Bilaterally Truncated Cauchy Distribution

设{X_k,1≤k≤n}独立同分布,服从参数为μ,λ;A,B的双截尾柯西分布,X_(1,n),X_(2,n),…,X_(n,n)为其顺序统计量.本文给出X_(k,n)(1≤k≤n)的密度函数,X_(1,n),X_(2,n),…,X_(n,n)的联合密度函数,极端顺序统计量X_(1,n)和X_(n,n)的渐近分布以及X_(k,n)和X_(n-k+1,n)(k>1)的渐近分布,并证明X_(1,n)和X_(n,n)是渐近独立的.

Let {X_k,1 ≤k ≤n}be independent and identically distributed random variables with bilaterally truncated Cauchy distribution of parametersμ,λ,A,B,X_(1,n),X_(2,n),…,X_(n,n)be their order statistics.In this paper we obtain the density function of X_(k,n),the joint density function of X_(1,n),X_(2,n),…,X_(n,n),the asymptotic distributions of their extreme order statistics X_(1,n) and X_(n,n),and the asymptotic distributions of Xk,nand X_(n-k+1,n).We also show that X_(1,n)and X_(n,n)is asymptotically independent.