关键词： 双截尾Cauchy分布, 参数估计, 顺序统计量

Abstract:

Suppose {X_k,1≤k≤n} are independent and all obey double truncated Cauchy distribution with μ,λ,A,B  as its parameters.This article obtains the nature of parameters of torque estimation.And it also provids numerical methods of parameters A,B's torque estimation when parameters μ,λ  are known.Moreover,parameters A,B's maximum likelihood estimation is obtained and  the other parameters' existence and strong combination of maximum likelihood estimation is proved.Eventually,asymptotic distribution of extreme order statistics is used to obtain the approximate interval estimation of parameters A,B.

Key words: double truncated Cauchy distribution, parameter estimation, order statistics