| 摘要: |
| 给定来自一未知连续分布函数F的容量为n的子样x1,x2,…,xn,考虑分布函数F的不变估计问题.在非对称损失函数L(F(t),d(t))=b∫(exp{a[d(t)-F(t)]}-a[d(t)-F(t)]-1)dF(t)和单调变换群下得到F的最优不变估计为d(t,X)=∑i=0nciI(x(i)≤ t ≤ x(i+1)),其中ci=1/aln(∫01ti(1-t)n-idt)/(∫01exp{-at}ti(1-t)n-idt),a≠0,b>0. |
| 关键词: 非对称损失 连续分布函数 不变估计 |
| DOI： |
| 投稿时间：2007-05-29 |
| 基金项目: |
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| Estimation of Distribution Function Under an Unsymmetrical Loss Fuction |
|
YU Hui-min
|
| (College of Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524088, China) |
| Abstract: |
| Given a random sample of x1, x2, …, xn size n from an unknown continuous distribution function F, this paper considers the problem of invariant estimator of the continuous distribution function F.Under the unsymmetrical loss function L (F (t), d (t))=b∫ (exp{a[d (t)-F (t)]}-a[d (t)-F (t)]-1)dF (t), we get the best invariant estimator of the continuous distribution function F. |
| Key words: unsymmetrical loss continuous distribution function invariant estimator |
