论文标题
带有截断点的左截断对数分布的最大似然估计
Maximum likelihood estimation for left-truncated log-logistic distributions with a given truncation point
论文作者
论文摘要
从数学角度和数值角度详细分析了左截断的对数分布分布的最大似然估计。这些最大似然方程通常也没有解决方案，即使对于小截断也是如此。为存在常规最大似然解决方案提供了简单的标准。在这种情况下，可以构建配置文件的可能性函数，并将优化问题降低到一个维度。当最大似然方程不接受某些数据样本的解决方案时，帕累托分布是退化的左截断对数分布的$ l^1 $限制。使用此数学信息，进行了高效的蒙特卡洛模拟，以获得一些拟合优点测试的临界值。提供了置信表和插值公式，并提供了几种对现实世界数据的应用程序。
The maximum likelihood estimation of the left-truncated log-logistic distribution with a given truncation point is analyzed in detail from both mathematical and numerical perspectives. These maximum likelihood equations often do not possess a solution, even for small truncations. A simple criterion is provided for the existence of a regular maximum likelihood solution. In this case a profile likelihood function can be constructed and the optimisation problem is reduced to one dimension. When the maximum likelihood equations do not admit a solution for certain data samples, it is shown that the Pareto distribution is the $L^1$-limit of the degenerated left-truncated log-logistic distribution. Using this mathematical information, a highly efficient Monte Carlo simulation is performed to obtain critical values for some goodness-of-fit tests. The confidence tables and an interpolation formula are provided and several applications to real world data are presented.
