定数截尾指数分布参数的最短区间估计

设随机变量Ｘ服从指数分布ｆ（ｘ，θ）＝１θｅ－ｘθｘ≥００ｘ＜０｛且Ｘ（１）≤Ｘ（２）≤…≤Ｘ（ｒ）为替换定数截尾子样，ｎ为投试样品个数（ｒ≤ｎ）。研究了具有一致最小平均长度的区间估计。给出了指数分布平均寿命参数θ的具有一致最小平均长度的区间估计为２ｒ＾θｒ，ｎＸ２Ｐ１（２ｒ）≤θ≤２ｒ＾θｒ，ｎＸ２Ｐ２（２ｒ）。相应地，指数分布平均失效率参数λ＝１θ的具有一致最小平均长度的区间估计为：Ｘ２１－α（１－１ｔ０）（２ｒ）２ｒ＾θｒ，ｎ≤λ＝１θ≤Ｘ２αｔ０（２ｒ）２ｒ＾θｒ，ｎ，同时给出了具有一致最小平均长度区间估计的计算方法和数值用表。

Interval Estimation of Exponential Distribution Parameters of Possessing Minimum Length Based on Censored Data

Let random variable x obey exponential distribution f(x,θ)=1θ e -xθ x≥0 0 x<0 X (1) ≤X (2) ≤ … ≤X (r ) be replacement data based on censored sample,and n be sample size (r≤n ). Interval estimation of exponential distribution parameters of possessing minimum length based on censored data is studied. Interval estimation of mean life parameters θ of exponential distribution based on censored data is presented, that is: 2r X 2 P 1 (2r)≤θ≤2r X 2 P 2 (2r) and interval estimation of mean false rate parameters λ= 1θ ,is X 2 1-α(1-1t 0) (2r)2r ≤λ=1θ≤X 2 αt 0 (2r)2r r,n ,correspondingly, method of numerical calculation and numerical data table given.