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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (4): 493-500    DOI:
    
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
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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-$t$     
Received: 25 March 2017      Published: 01 December 2018
CLC:  O213.2  
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WANG Bing-xing
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Cite this article:

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.

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


Gamma分布环境因子的统计分析

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-$t$ 
[1] ZHOU Jun-xing, YU Lie-hong, WANG Bing-xing. Statistical inference for the environment factor under exponential and Weibull series system[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(1): 1-8.