Abstract:

 Let {X_k,1≤k ≤n}be independent and identically distributed random variables with bilaterally truncated Cauchy distribution of parameters μ,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 X_k,n and X_n-k+1,n.We also show that X_1,n and X_n,n is asymptotically independent.

Key words:

Bilaterally truncated Cauchy distribution, Order statistic, Asymptotic distribution, Asymptotical independence