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首页> 外文学位 >Simulating univariate and multivariate Burr Type III and Type XII distributions through the method of L-moments.
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Simulating univariate and multivariate Burr Type III and Type XII distributions through the method of L-moments.

机译：通过L矩方法模拟单变量和多变量Burr III型和XII型分布。

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摘要

The Burr families (Type III and Type XII) of distributions are traditionally used in the context of statistical modeling and for simulating non-normal distributions with moment-based parameters (e.g., Skew and Kurtosis). In educational and psychological studies, the Burr families of distributions can be used to simulate extremely asymmetrical and heavy-tailed non-normal distributions.;Conventional moment-based estimators (i.e., the mean, variance, skew, and kurtosis) are traditionally used to characterize the distribution of a random variable or in the context of fitting data. However, conventional moment-based estimators can (a) be substantially biased, (b) have high variance, or (c) be influenced by outliers. In view of these concerns, a characterization of the Burr Type III and Type XII distributions through the method of L-moments is introduced. Specifically, systems of equations are derived for determining the shape parameters associated with user specified L-moment ratios (e.g., L-Skew and L-Kurtosis). A procedure is also developed for the purpose of generating non-normal Burr Type III and Type XII distributions with arbitrary L-correlation matrices. Numerical examples are provided to demonstrate that L-moment based Burr distributions are superior to their conventional moment based counterparts in the context of estimation, distribution fitting, and robustness to outliers.;Monte Carlo simulation results are provided to demonstrate that L-moment-based estimators are nearly unbiased, have relatively small variance, and are robust in the presence of outliers for any sample size. Simulation results are also provided to show that the methodology used for generating correlated non-normal Burr Type III and Type XII distributions is valid and efficient. Specifically, Monte Carlo simulation results are provided to show that the empirical values of L-correlations among simulated Burr Type III (and Type XII) distributions are in close agreement with the specified L-correlation matrices.
机译：传统上，分布的Burr族（III型和XII型）用于统计建模和模拟基于矩的参数（例如Skew和Kurtosis）的非正态分布。在教育和心理学研究中，伯尔分布族可用于模拟极不对称且重尾的非正态分布。传统上基于矩量的估计量（即均值，方差，偏度和峰度）通常用于表征随机变量的分布或拟合数据。但是，传统的基于矩的估计量可能会（a）受到严重偏见，（b）具有高方差，或者（c）受异常值的影响。考虑到这些问题，介绍了通过L矩方法表征Burr III型和XII型分布的方法。具体地，导出方程式系统以确定与用户指定的L力矩比（例如，L-Skew和L-Kurtosis）相关的形状参数。还开发了一种程序，用于生成具有任意L相关矩阵的非正态Burr类型III和XII类型分布。数值算例表明，基于L矩的Burr分布在估计，分布拟合和离群值的鲁棒性方面优于传统基于矩的Burr分布;提供了蒙特卡罗仿真结果以证明基于L矩的Burr分布估计量几乎是无偏的，方差相对较小，并且在存在任何样本量的异常值时都具有鲁棒性。仿真结果还表明，用于生成相关的非正态Burr III型和XII型分布的方法是有效和高效的。具体而言，提供的蒙特卡罗模拟结果表明，模拟的Burr III型（和XII型）分布中的L相关性的经验值与指定的L相关性矩阵非常一致。

著录项

  • 作者

    Pant, Mohan Dev.;

  • 作者单位

    Southern Illinois University at Carbondale.;

  • 授予单位 Southern Illinois University at Carbondale.;
  • 学科 Education Tests and Measurements.;Education Educational Psychology.;Statistics.
  • 学位 Ph.D.
  • 年度 2011
  • 页码 87 p.
  • 总页数 87
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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