摘要
文章对Gumbel Type-Ⅱ分布进行了推广,提出一种新的四参数Gumbel分布,称作Marshall-Olkin Alpha Power Gumbel Type-Ⅱ(MOAPGT-Ⅱ)分布,推导了MOAPGT-Ⅱ分布的一些基本统计性质,如生存函数、风险函数以及反风险函数等.此外,运用极大似然估计给出了MOAPGT-Ⅱ分布的参数估计,分别对不同大小的样本进行蒙特卡洛模拟分析,结果表明估计值的均方误差和绝对偏差都比较小.最后用一个真实的数据集解释MOAPGT-Ⅱ分布的适用性,结果表明MOAPGT-Ⅱ分布比文献中已有的竞争分布有更好的拟合.
A new Gumbel Type-Ⅱ distribution with four parameters,called Marshall-Olkin Alpha Power Gumbel Type-Ⅱ(MOAPGT-Ⅱ)distribution,is proposed.Some basic statistical properties of MOAPGT-Ⅱ distribution,such as survival function,risk function and anti-risk function,are derived.In addition,the parameter estimation of MOAPGT-Ⅱ distribution is given by using maximum likelihood,and Monte Carlo simulation is carried out for different sample sizes.The results show that the mean square error and absolute deviation of the estimation values are relatively small.Finally,a real data set is used to explain the applicability of the MOAPGT-Ⅱ distribution.The results show that the MOAPGT-Ⅱ distribution can be fitted better than the competing distribution in the literature.
作者
程月
田茂再
CHENG Yue;TIAN Mao Zai(School of Statistics and Data Science,Xinjiang University of Finance and Economics,Wulumuqi 830012,China;Research Center of Applied Statistics,Renmin University of China,Beijing 100190,China)
出处
《河南科技学院学报（自然科学版）》
2023年第6期39-47,共9页
Journal of Henan Institute of Science and Technology(Natural Science Edition)
基金
国家自然科学基金(11861042)。
