Length-biased distributions arise naturally in environmental, reliability, and economic studies where the sampling mechanism favors larger observational units. In this paper, we propose a quantile regression model based on the length-biased Birnbaum--Saunders (QLBS) distribution. The model is constructed through a reparameterization of the length-biased Birnbaum--Saunders distribution in terms of its quantile function, thereby allowing direct interpretation of covariate effects on conditional quantiles of the response variable. We derive the log-likelihood function and the corresponding score equations, and obtain maximum likelihood estimators via numerical optimization. Asymptotic and bootstrap confidence intervals are considered. Two types of residuals are proposed for model assessment, namely the generalized Cox--Snell and randomized quantile residuals. An elaborate Monte Carlo simulation study is carried out to evaluate the performance of the maximum likelihood estimators for several sample sizes and quantile levels. The proposed methodology is illustrated with a real meteorological data set from Brazil.

翻译：长度偏差分布自然产生于环境、可靠性和经济学研究中，当抽样机制偏向于更大的观测单元时。本文提出了一种基于长度偏差Birnbaum-Saunders（QLBS）分布的分位数回归模型。该模型通过重新参数化长度偏差Birnbaum-Saunders分布的分位数函数来构建，从而直接解释协变量对响应变量条件分位数的影响。我们推导了对数似然函数及其相应的得分方程，并通过数值优化获得了极大似然估计量。考虑了渐近置信区间和Bootstrap置信区间。为模型评估提出了两种残差类型，即广义Cox-Snell残差和随机化分位数残差。通过详尽的蒙特卡洛模拟研究评估了不同样本量和分位数水平下极大似然估计量的性能。所提出的方法以来自巴西的真实气象数据集进行了说明。