Abstract

We propose two new regressions based on the generalized odd log-logistic log-normal distribution allowing for positive and negative skewness to model bimodal data. The first one is the parametric regression and the second one is an additive partial linear regression. The new regressions aim to estimate the linear and non-linear effects of covariables on the response variable and generalize some existing regressions in the literature. For both cases, the model parameters are estimated by the methods of maximum likelihood and maximum penalized likelihood. In particular, a model check based on the quantile residuals is used to select the appropriate covariables. We reanalyze two data sets, one for each proposed regression.

摘要

我们提出了两个基于广义奇数逻辑对数正态分布的新回归，允许正偏度和负偏度对双峰数据进行建模。第一个是参数回归，第二个是加性偏线性回归。新的回归旨在估计协变量对响应变量的线性和非线性影响，并概括文献中的一些现有回归。对于这两种情况，模型参数都是通过最大似然法和最大惩罚似然法估计的。特别是，基于分位数残差的模型检查用于选择适当的协变量。我们重新分析两个数据集，一个用于每个建议的回归。