基于偏斜分布和相关EM估计的多元Birnbaum-Saunders分布

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
F. Vilca, Camila Borelli Zeller, N. Balakrishnan
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引用次数: 0

摘要

在多元斜正态分布的基础上,我们发展了Birnbaum-Saunders(BS)分布的多元推广。通过所提出模型的层次表示,给出了一些分布特征和性质,以及一种简单有效的EM算法,用于迭代计算模型参数的最大似然(ML)估计。根据观测到的Fisher信息矩阵计算最大似然估计的标准误差。此外,通过使用这些工具,我们提出了一个对数线性回归模型,其中使用EM算法再次获得ML估计。最后,给出了仿真研究和两个对真实数据集的应用,以说明本文建立的模型和推理结果。缩写列表AIC Akaike信息标准BS Birnbaum-Saunders BVBS双变量Birnbaum Saunders cdf累积分布函数CI置信区间CM条件最大化ECM期望条件最大化EM期望最大化LR似然比ML最大似然MSE均方根误差NBS非中心Birnbaum-Saunders pdf概率密度函数RB相对偏差SD标准偏差SE标准误差SIC Schwarz信息标准SMN正态SN比例混合正态SNBS正态Birnbaum-Saunders TTT总测试时间
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Multivariate Birnbaum–Saunders distribution based on a skewed distribution and associated EM-estimation
We develop here a multivariate generalization of Birnbaum-Saunders (BS) distribution based on the multivariate skew-normal distribution. Some distributional characteristics and properties are presented, as well as a simple and efficient EM algorithm for the iterative computation of the maximum likelihood (ML) estimates of model parameters, through the hierarchical representation of the proposed model. The standard errors of the maximum likelihood estimates are calculated from the observed Fisher information matrix. Moreover, by using the tools, we present a log-linear regression model, where the the ML estimates are once again obtained using an EM algorithm. Finally, simulation studies and two applications to real data sets are presented for illustrating the model and the inferential results developed here. List of Abbreviations AIC Akaike information criterion BS Birnbaum-Saunders BVBS Bivariate Birnbaum-Saunders cdf cumulative distribution function CI Confidence Interval CM Conditional Maximization ECM Expectation-Conditional Maximization EM Expectation-Maximization LR Likelihood Ratio ML Maximum Likelihood MSE root Mean Squared Error NBS Non-Central Birnbaum-Saunders pdf probability density function RB Relative Bias SD Standard Deviation SE Standard Error SIC Schwarz information criterion SMN Scale Mixtures of Normal SN Skew-Normal SNBS Skew-Normal Birnbaum-Saunders TTT Total Time on Test
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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