A novel approach to adding an additional parameter to a family of distributions for better adaptability has been put forth. This approach yields a versatile class of distributions supported on the positive real line. An important advantage of the proposed family is that the additional parameter admits a clear interpretation in terms of tail behavior, providing a simple mechanism for modulating tail heaviness. We proceed to analyze its mathematical characteristics, such as critical points, modality, stochastic representation, identifiability, quantiles, moments, and truncated moments. We present two new regression models for positive continuous data based on submodels of the newly proposed family of distributions, in which the distribution of the response variable is reparameterized in terms of the median. We use the maximum likelihood method to estimate the parameters, which was implemented through the gamlss package in R. The proposed regression models were applied to a real dataset, and their advantages over common alternative regression models were demonstrated through quantile residual analysis and information criteria.

翻译：提出了一种通过向分布族添加额外参数以增强适应性的新方法。该方法生成了一类支持在正实数轴上的多用途分布族。该分布族的一个重要优势在于，额外参数在尾部行为方面具有明确解释，为调节尾部厚度提供了简单机制。我们进一步分析了其数学性质，包括临界点、模态、随机表示、可识别性、分位数、矩以及截断矩。基于新分布族的子模型，我们提出了两种适用于正连续数据的新回归模型，其中响应变量的分布以中位数重新参数化。采用最大似然法估计参数，并通过R语言的gamlss包实现。将所提出的回归模型应用于实际数据集，通过分位残差分析和信息准则证明了其相对于常用替代回归模型的优势。