We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its parameters, estimation reduces to constrained linear regression, yielding a convex optimization problem that readily accommodates cardinality constraints as well as L1 or smoothness regularization. For Lq-type objectives we show the estimator is asymptotically equivalent to a minimum q-Wasserstein distance estimator and establish asymptotic normality. Experiments on simulated and real-world datasets demonstrate that the proposed method accurately captures both the central body and extreme tails of distributions while requiring substantially less computation than standard benchmark approaches.

翻译：本文研究通过分位数函数建模单变量分布的问题。我们提出一类灵活的概率分布族，其分位数函数可表示为基分位数的线性组合。由于该模型在参数上呈线性关系，估计问题可转化为约束线性回归，从而得到一个凸优化问题，该问题能够自然地容纳基数约束以及L1或平滑正则化。对于Lq型目标函数，我们证明该估计量渐近等价于最小q-瓦瑟斯坦距离估计量，并建立了渐近正态性。在模拟和真实数据集上的实验表明，所提方法能够准确捕捉分布的中心主体与极端尾部特征，同时所需计算量显著低于标准基准方法。