论文标题
Weibull分布和属性参数的最大$ \ log_q $估计：蒙特卡洛模拟
Maximum $\log_q$ Likelihood Estimation for Parameters of Weibull Distribution and Properties: Monte Carlo Simulation
论文作者
论文摘要
最大$ {\ log} _q $ ibilihood估计方法是对已知的最大$ \ log $ libileahie方法的概括，以克服建模非相同观测值（Inliers and Outliers和Outliers）的问题。参数$ Q $是管理建模功能的调谐常数。威布尔（Weibull）是工程问题的灵活且流行的分布。在这项研究中，当存在非相同观察结果时，该方法用于估计Weibull分布的参数。由于主要思想是基于目标函数的建模能力$ρ（x; \boldsymbolθ）= \ log_q \ big [f（x; \boldsymbolθ）\ big] $，因此我们观察到得分函数的有限性在Inliers的可靠估计中不能起作用。研究了Weibull分布的属性。在数值实验中，如果应用了$ \ log_q $及其特殊形式$ \ log $，可能性方法，则Weibull分布的参数估计，如果应用于基础Weibull分布的不同设计。优化是通过遗传算法进行的。蒙特卡洛模拟观察到了$ρ（x; \boldsymbolθ）$的建模能力和对非相同观察的不敏感性。 $ Q $的值可以通过在模拟中使用平方误差以及用于评估拟合能力的Kolmogorov-Smirnov测试统计量的$ p $ - 值。因此，我们可以克服有关确定实际数据集$ Q $值的问题。
The maximum ${\log}_q$ likelihood estimation method is a generalization of the known maximum $\log$ likelihood method to overcome the problem for modeling non-identical observations (inliers and outliers). The parameter $q$ is a tuning constant to manage the modeling capability. Weibull is a flexible and popular distribution for problems in engineering. In this study, this method is used to estimate the parameters of Weibull distribution when non-identical observations exist. Since the main idea is based on modeling capability of objective function $ρ(x;\boldsymbolθ)=\log_q\big[f(x;\boldsymbolθ)\big]$, we observe that the finiteness of score functions cannot play a role in the robust estimation for inliers. The properties of Weibull distribution are examined. In the numerical experiment, the parameters of Weibull distribution are estimated by $\log_q$ and its special form, $\log$, likelihood methods if the different designs of contamination into underlying Weibull distribution are applied. The optimization is performed via genetic algorithm. The modeling competence of $ρ(x;\boldsymbolθ)$ and insensitiveness to non-identical observations are observed by Monte Carlo simulation. The value of $q$ can be chosen by use of the mean squared error in simulation and the $p$-value of Kolmogorov-Smirnov test statistic used for evaluation of fitting competence. Thus, we can overcome the problem about determining of the value of $q$ for real data sets.
