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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (4): 493-500    
    
Gamma分布环境因子的统计分析
王炳兴1, 吴方涛1, 周君兴2
1. 浙江工商大学统计与数学学院, 浙江杭州310018;
2. 浙江财经大学数据科学学院, 浙江杭州310018
Statistical analysis for the environment factor under the gamma distribution
WANG Bing-xing1, WU Fang-tao1, ZHOU Jun-xing2
1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China;
2. School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou 310018, China
 全文: PDF 
摘要： 证明了Gamma分布环境因子的最大似然估计是有偏估计, 且其偏差为正, 进而导出了Gamma分布环境因子的近似无偏估计. 利用Cornish-Fisher展开导出了Gamma分布环境因子的广义置信区间, 另外也给了Gamma分布环境因子的Bootstrap-$t$置信区间. 利用模拟方法研究了所给近似无偏估计和区间估计的精度, 模拟结果显示所给近似无偏估计和区间估计的精度是相当好的.
关键词： 环境因子;  Gamma分布;  Cornish-Fisher展开;  广义置信区间;  Bootstrap-$t$    
Abstract: It is verified that the maximum likelihood estimation of the environment factor for the gamma distribution is biased, and that its bias is positive. Then an approximate unbiased estimation of the environment factor is derived. Using the Cornish-Fisher expansion, the generalized confidence interval of the environment factor is proposed. The bootstrap-$t$ confidence interval is also given. The performance of the proposed procedures is evaluated by using Monte Carlo simulation. The simulation results show that the proposed point estimation outperforms the MLE and that the coverage percentages of the proposed generalized confidence interval are quite close to the nominal coverage probabilities, even for small sample size and for small shape parameter.
Key words: environment factor    Gamma distribution    Cornish-Fisher expansion    generalized confidence interval    Bootstrap-$t$
收稿日期: 2017-03-25 出版日期: 2018-12-01
CLC:  O213.2  
基金资助: 国家自然科学基金(11371322; 11671303); 浙江省一流学科A类(浙江工商大学统计学)
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引用本文:

王炳兴, 吴方涛, 周君兴. Gamma分布环境因子的统计分析[J]. 高校应用数学学报, 2017, 32(4): 493-500.

WANG Bing-xing, WU Fang-tao, ZHOU Jun-xing. Statistical analysis for the environment factor under the gamma distribution. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 493-500.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I4/493

[1] 周君兴, 俞列红, 王炳兴. 指数和Weibull串联系统环境因子的统计推断[J]. 高校应用数学学报, 2016, 31(1): 1-8.