Building on recent developments in models focused on the shape properties of odds ratios, this paper introduces two new models that expand the class of available distributions while preserving specific shape characteristics of an underlying baseline distribution. The first model offers enhanced control over odds and logodds functions, facilitating adjustments to skewness, tail behavior, and hazard rates. The second model, with even greater flexibility, describes odds ratios as quantile distortions. This approach leads to an enlarged log-logistic family capable of capturing these quantile transformations and diverse hazard behaviors, including non-monotonic and bathtub-shaped rates. Central to our study are the shape relations described through stochastic orders; we establish conditions that ensure stochastic ordering both within each family and across models under various ordering concepts, such as hazard rate, likelihood ratio, and convex transform orders.

翻译：基于近期针对优势比形态特性模型的研究进展，本文提出了两种新模型，它们在保持基础基准分布特定形态特征的同时，扩展了可用分布的类别。第一个模型增强了对优势函数与对数优势函数的控制能力，便于调整偏度、尾部行为与风险率。第二个模型具有更高的灵活性，将优势比描述为分位数失真。该方法导出了一个扩展的对数逻辑分布族，能够捕捉这些分位数变换及多样的风险行为，包括非单调型与浴盆型风险率。我们研究的核心在于通过随机序描述的形态关系；我们建立了确保每个分布族内部以及不同模型之间在多种序概念（如风险率序、似然比序及凸变换序）下保持随机序的条件。