从噪声分位数数据估计具有失效率特性的分布
Estimating Distributions with Failure Rate Properties from Noisy Quantile Data
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中文总结 AI 辅助
研究从噪声分位数数据估计具有失效率特性的分布问题，提出IFR约束最大似然估计器，通过两步法解决，建立误差界和收敛速率，扩展到其他特性，经实验和案例研究提升了拟合度与决策质量。
中文摘要 AI 辅助
从数据中估计未知累积分布函数（cdf）在运营中至关重要，但实际中常因分布结构不完全了解和数据有限、受审查而复杂。本文研究满足失效率形状约束（特别是递增失效率（IFR））的分布，考虑噪声分位数数据。提出IFR约束最大似然估计器，其原问题是无限维非凸的。开发两步法，先解决变换节点值的有限维凸优化问题，再通过保形插值重构完整cdf。建立有限样本误差界和收敛速率，还扩展到其他失效率特性。数值实验和案例研究证明了良好拟合及下游决策质量提升。
英文摘要
Estimating an unknown cumulative distribution function (cdf) from data, either as a statistical object of interest or as an input to a downstream optimization problem, is fundamental in operations. In practice, however, distribution estimation is often complicated by incomplete knowledge of the distribution's structure and limited, censored data. To address the first complication, we study distributions satisfying failure-rate shape constraints, especially increasing failure rate (IFR), rather than assuming a fully specified parametric family. To address the second, we consider noisy quantile data: at finitely many prespecified knots, each observation records only whether an independent sample lies below or above the knot. This combination arises naturally in pricing, reliability, and healthcare applications. We formulate the IFR-constrained maximum likelihood estimator and show that the original problem is infinite-dimensional and non-convex. We then develop a tractable two-step approach that solves a finite-dimensional convex optimization problem over transformed knot values and reconstructs a full cdf through shape-preserving interpolation. We establish finite-sample error bounds and convergence rates, yielding practical guidance for offline data collection. We also extend the framework to failure-rate-average, new-better-than-used, and generalized-failure-rate properties. Numerical experiments and case studies in revenue management and reliability demonstrate strong goodness-of-fit and improved downstream decision quality.
