Alpha Power伽马分布的性质与应用  

Properties and Applications of Alpha Power Gamma Distribution

作　　者：牛郁琳 闫在在[1] NIU Yulin;YAN Zaizai(College of Science,Inner Mongolia University of Technology,Hohhot,010051,China)

机构地区：[1]内蒙古工业大学理学院

出　　处：《应用概率统计》2019年第4期331-344,共14页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11861049);内蒙古自然科学基金面上项目(批准号:2017MS0101、2018MS01027)资助

摘　　要：本文通过增加一个额外的形状参数,扩展了伽马分布,称这种新分布为alpha power伽马分布.发现该分布具有相对灵活的危险率函数.研究了它的性质,包括s阶原点矩、矩母函数以及次序统计量分布的显式表达.得到了熵、平均剩余寿命以及平均等待时间的积分表达.讨论了该分布在完全样本下参数的极大似然估计,得到了参数的Fisher信息矩阵.进一步,研究了一般Ⅱ型逐次截尾样本下的参数估计.最后通过一个实际数据分析说明了提出分布的实用性.In this paper, the gamma distribution has been extended by adding an extra shape parameter, we refer to the new distribution as alpha power gamma distribution. It is found that the distribution has a relatively flexible hazard rate function. The properties of the new distribution are studied, including explicit expressions for the s^th raw moments, moment generating function and distributions of order statistics are derived. Also, the integral expressions for the entropy, mean residual life and mean waiting time are obtained. The maximum likelihood estimators of the distribution parameters under complete sample are discussed, the Fisher information matrix is derived. Then, the estimation of the parameters under the general progressive type-Ⅱ censoring is studied. Finally, the real data set is used to illustrate the practicality of the proposed distribution.

关 键 词：ALPHA POWER TRANSFORMATION 伽马分布 极大似然估计 Fisher信息矩阵 一般Ⅱ型逐次截尾 

分 类 号：O213.2[理学—概率论与数理统计]