二参数的条件指数型威布尔分布的最大值吸引场
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摘要
对二参数Exponential-Weibull的条件分布的最大值吸引场类型进行了研究.首先判断了Exponential-Weibull的条件分布的最大值吸引场类型,并给出了此分布的最大值吸引场条件下的规范化常数的表达式,最后通过数值模拟,检验了规范化常数的准确性,这为研究最大值吸引场的其它性质奠定基础,也是进行最大值吸引场条件下的估计的前提.
In this paper, the maximum domain of attraction of the two-parameter conditional Exponential-Weibull distribution is studied. The conditional Exponential-Weibul distribution is confirmed and proven to belong to the maximum domain of attraction of the Gumbel distribution, and the expressions of the corresponding normalizing constants are derived. Numerical simulations are conducted to investigate the performance of the proposed normalizing constants. This lays the foundation for studying the other properties of the maximum domain of attraction, and is also the premise for estimating the maximum domain of attraction.
In this paper, the maximum domain of attraction of the two-parameter conditional Exponential-Weibull distribution is studied. The conditional Exponential-Weibul distribution is confirmed and proven to belong to the maximum domain of attraction of the Gumbel distribution, and the expressions of the corresponding normalizing constants are derived. Numerical simulations are conducted to investigate the performance of the proposed normalizing constants. This lays the foundation for studying the other properties of the maximum domain of attraction, and is also the premise for estimating the maximum domain of attraction.
引文
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[13]魏艳华,王丙参,邢永忠.指数-威布尔分布参数贝叶斯估计的混合Gibbs算法[J].统计与决策,2017(16):70-73.
[14]李建丽,李海增,李江杰.恒加应力水平下混合指数-威布尔分布的EM估计[J].长治学院学报,2017,34(16):28-29.
[15]包振华,张姝.基于指数威布尔分布的组合统计模型[J].统计与决策,2018, 34(1):10-13.
[16]黄傲林,叶灵军.基于威布尔分布的舰船装备故障分析[J].舰船电子工程,2007(1):180-202.
[17]王战胜.基于exponentiated Weibull模型的无线光通信LDPC信道编码技术研究[D].西安电子科技大学,2014.
[18] Zacks S. Estimating the shift to wear-out of systems having exponential-weibull life distributions[J].Operations Research, 1984, 32(3):741-749.
[19]史道济.实用极值统计方法[M].天津科学技术出版社,2006:1-202.
[2] Mudholkar G S, Srivastava D K,Marshall Freimer. The exponentiated Weibull family:a reanalysis of the bus-motor-failure data[J]. Technometrics, 1995, 37(4):436-445.
[3] Mudholkar G S, Hutson A D. The exponentiated weibull family:some properties and a flood data application[J]. Communications in Statistics-Theory and Methods, 1996, 25(12):3059-3083.
[4] Pal M, Ali M M, Woo J. Exponentiated-Weibull Distribution[J]. Statistica, 2006, 66(2):139-147.
[5] Tibor Nanasi. Interval censored data analysis with Weibull and exponential distribution[J]. Applied Mechanics and Materials, 2014, 3592(693):74-79.
[6] Cordeiro G M, Ortega E M M, Lemonte A J. The exponential-Weibull lifetime distribution[J].Journal of Statistical Computation and Simulation, 2014, 84(12):2592-2606.
[7] Khan R U, Kulshrestha A, Khan M A. Relations for moments of k-th record values from exponentialWeibull lifetime distribution and a characterization[J]. Journal of the Egyptian Mathematical Society, 2015, 23(3):558-562.
[8]冯艳,师义民,严惠云.定数截尾两参数指数——威布尔分布形状参数的Bayes估计[J].数学的实践与认识,2007, 37(5):65-71.
[9]张晓勤,王煜,卢殿军.混合指数威布尔分布的参数估计[J].河南大学学报(自然科学版),2012, 42(3):230-233.
[10]邢务强,师义民.Ⅰ型混合截尾下指数-威布尔分布的统计分析[J].火力与指挥控制,2013, 38(5):55-61.
[11]崔群法,张明亮,康会光.LINER损失下参数未知时指数-威布尔分布的Bayes估计[J].河南大学学报(自然科学版),2011(4):348-351.
[12]程从华,陈进源,李泽慧.基于删失数据的指数威布尔分布最大似然估计的新算法(英文)[J].应用数学,2010, 23(3):638-647.
[13]魏艳华,王丙参,邢永忠.指数-威布尔分布参数贝叶斯估计的混合Gibbs算法[J].统计与决策,2017(16):70-73.
[14]李建丽,李海增,李江杰.恒加应力水平下混合指数-威布尔分布的EM估计[J].长治学院学报,2017,34(16):28-29.
[15]包振华,张姝.基于指数威布尔分布的组合统计模型[J].统计与决策,2018, 34(1):10-13.
[16]黄傲林,叶灵军.基于威布尔分布的舰船装备故障分析[J].舰船电子工程,2007(1):180-202.
[17]王战胜.基于exponentiated Weibull模型的无线光通信LDPC信道编码技术研究[D].西安电子科技大学,2014.
[18] Zacks S. Estimating the shift to wear-out of systems having exponential-weibull life distributions[J].Operations Research, 1984, 32(3):741-749.
[19]史道济.实用极值统计方法[M].天津科学技术出版社,2006:1-202.