We introduce a family of distributions with bounded support for continuous rates or proportions when the data contain zeros or ones. On the basis of this class of distributions, we propose a novel class of regression models which is useful for modelling fractional data observed on [0, 1) or (0, 1]. The response variable of the new class of regression models has a mixed continuous-discrete distribution with probability mass at zero or one, and the parameters of the mixture distribution are modelled through regression structures involving covariates and unknown parameters. An advantage of this class of regression models is the ability to deal with atypical observations. We consider a frequentist approach to performing inferences, and the traditional maximum likelihood method is employed to estimate the regression parameters. We also propose a residual analysis for the novel class of regression models to assess departures from model assumptions. Additionally, global and local influence methods are discussed. An empirical application that employs real data is considered to illustrate the usefulness of the new class of regression models in practice.

中文翻译：

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比率和比例的一类广泛的零或一膨胀回归模型

当数据包含零或一时，我们引入了对连续比率或比例有界支持的分布族。在这类分布的基础上，我们提出了一类新的回归模型，它可用于对在 [0, 1) 或 (0, 1] 上观察到的分数数据进行建模。新类回归模型的响应变量具有概率质量为零或一的混合连续离散分布，混合分布的参数通过涉及协变量和未知参数的回归结构建模。这类回归模型的一个优点是能够处理非典型观察。我们认为执行推理的频率论方法，并采用传统的最大似然方法来估计回归参数。我们还建议对新型回归模型进行残差分析，以评估对模型假设的偏离。此外，还讨论了全局和局部影响方法。考虑使用真实数据的经验应用来说明新类别回归模型在实践中的有用性。