Alpha偏幂正态分布及其应用  

Alpha Skew Power Normal Distribution and Its Application

作　　者：魏正元 彭天奎 周晓娅 WEI Zhengyuan;PENG Tiankui;ZHOU Xiaoya(College of Science,Chongqing University of Technology,Chongqing,400054,China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《应用概率统计》2022年第5期647-658,共12页Chinese Journal of Applied Probability and Statistics

基　　金：重庆市自然科学基金项目(批准号:cstc2020jcyj-msxmX0232、cstc2019jcyj-msxmX0386);重庆市高等教育教学改革研究项目(批准号:203332);重庆理工大学研究生创新项目(批准号:clgycx20202114)资助。

摘　　要：提出了一类新的alpha偏幂正态分布,使得alpha偏正态分布和幂正态分布是其特例.给出了该新分布的矩、偏度、峰度、Fisher信息阵以及参数的最大似然估计量、随机数的产生算法等.大量的随机模拟试验表明,参数最大似然估计量具有较好的渐近统计性质,且对一组真实数据集的分布拟合结果显示,alpha偏幂正态分布比正态分布、偏正态分布、幂正态分布和alpha偏正态分布的拟合效果更好.A new class of alpha skew power normal distribution is proposed,such that alpha skew normal distribution and power normal distribution are special cases.Its moment,skewness,kurtosis,Fisher information matrix,maximum likelihood estimator and the generation algorithm of random number are given.Extensive simulation experiments show that the maximum likelihood estimator of parameters has good asymptotic statistical properties,the distribution fitting results of a group of real data sets show that alpha skew power normal distribution has better fitting effect than normal distribution,skew normal distribution,power normal distribution and alpha skew normal distribution.

关 键 词：alpha偏幂正态分布 偏度 FISHER信息阵 最大似然估计量 

分 类 号：O211.3[理学—概率论与数理统计]