Kumaraswamy Marshall-Olkin Rayleigh分布的统计分析
Statistical Analysis of Kumaraswamy Marshall-Olkin Rayleigh Distributions
DOI: 10.12677/aam.2024.137329, PDF,    科研立项经费支持
作者: 李俊华：汉江师范学院数学与计算机科学学院，湖北 十堰
关键词: KwMO扩展；Rayleigh分布；极大似然估计；Monte-Carlo算法；KwMO Extension Method； Rayleigh Distribution； The Maximum Likelihood Estimation； Monte-Carlo Algorithm
摘要: 文章通过Kumaraswamy Marshall-Olkin扩展，将Rayleigh分布扩展为一个新的具有四参数的分布Kumaraswamy Marshall-Olkin Rayleigh (KwMO-R)分布，然后计算了该分布的矩、危险率函数、Renyi熵、次序统计量的极限分布以及参数的极大似然估计，并验证了估计的相合性，最后利用Monte-Carlo算法对参数的估计进行了数值模拟。
Abstract: In this paper, through the Kumaraswamy Marshall-Olkin extension, the Rayleigh distribution is extended to a new distribution with four parameters. Then, the moment, risk function, Renyi entropy, limit distribution of order statistics and maximum likelihood estimation of the parameters are calculated, and the consistency of the estimation is verified. Finally, the parameter estimation is simulated by Monte-Carlo algorithm.
文章引用：李俊华. Kumaraswamy Marshall-Olkin Rayleigh分布的统计分析[J]. 应用数学进展, 2024, 13(7): 3433-3441. https://doi.org/10.12677/aam.2024.137329

参考文献

[1] Eugene, N., Lee, C. and Famoye, F. (2002) Beta-Normal Distribution and Its Applications. Communications in Statistics—Theory and Methods, 31, 497-512. [Google Scholar] [CrossRef] 
[2] Jones, M.C. (2004) Families of Distributions Arising from Distributions of Order Statistics. Test, 13, 1-43. [Google Scholar] [CrossRef] 
[3] Marshall, A. (1997) A New Method for Adding a Parameter to a Family of Distributions with Application to the Exponential and Weibull Families. Biometrika, 84, 641-652. [Google Scholar] [CrossRef] 
[4] Cordeiro, G.M., Ortega, E.M.M. and Nadarajah, S. (2010) The Kumaraswamy Weibull Distribution with Application to Failure Data. Journal of the Franklin Institute, 347, 1399-1429. [Google Scholar] [CrossRef] 
[5] Ramos, M.W.A. (2014) Some New Extended Distributions: Theory and Applications. Master’s Thesis, Universidade Federal de Pernambuco Recife.
[6] 刘焱哲, 贾俊梅, 闫在在. Kumaraswamy Marshall-Olkin Logistic Exponential 分布[J]. 数理统计与管理, 2020, 40(4): 654-670.
[7] 常帅, 关晋瑞, 姚仪婷. Kumaraswamy倒帕累托分布及其应用[J]. 数学的实践与认识, 2021, 51(11): 154-161.
[8] Gradshteyn, I.S. and Ryzhik, I.M. (2007) Table of Integrals, Series, and Products. 7th Edition, Academic Press.
[9] Nadarajah, S., Cordeiro, G.M. and Ortega, E.M.M. (2014) The Zografos-Balakrishnan-G Family of Distributions: Mathematical Properties and Applications. Communications in Statistics—Theory and Methods, 44, 186-215. [Google Scholar] [CrossRef] 
[10] Galambos, J. (2001) The Asymptotic Theory of Extreme Order Statistics. 2nd Edition, China Science Press.
[11] Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977) Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society Series B: Statistical Methodology, 39, 1-22. [Google Scholar] [CrossRef] 
[12] Hamedani, G.G., Javanshiri, Z., Maadooliat, M. and Yazdani, A. (2014) Remarks on Characterizations of Malinowska and Szynal. Applied Mathematics and Computation, 246, 377-388. [Google Scholar] [CrossRef] 

为你推荐