南通大学学报（自然科学版）

Logistic分布是一种重要的位置-尺度分布,与正态分布比较,Logistic分布是一种厚尾分布.为刻画数据的异方差性,提出了基于Logistic分布的位置-尺度参数联合回归建模问题,利用牛顿迭代法得到了参数估计算法.为检验解释变量的重要性,基于Score检验方法研究了相关的假设检验问题,并通过数值模拟研究其检验功效问题.最后,利用AIC和BIC信息准则对基于Logistic回归模型和线性回归进行拟合优度分析.大量数值模拟和实例数据分析验证了所提方法的有效性.

Logistic distribution is an important location-scale distribution. Compared with the normal distribution, Logistic distribution is a heavy-tailed distribution. To describe the heteroskedasticity of data, a joint regression modeling method based on the Logistic distribution was proposed through using Newton method to get the parameter estimation algorithm. In order to test the importance of the explanatory variables, the related hypothesis testing problem based on the Score test method was explored, and the effectiveness of the test by simulation was studied. Finally, the AIC and BIC information criterion were used to analyze the goodness of fit of the Logistic regression and linear regression. A large number of numerical simulations and examples of data confirm its effectiveness.