This paper investigates some properties of the mixture models from the quantile residual life perspective. It is shown that a mixture model is bounded by its components via the quantile residual life. We investigate how mixture models are ordered in terms of the quantile residual life function when their components are ordered. Besides, we prove that the limiting quantile residual life of a mixture is similar to that of the greatest component at infinity. Based on these results, it is possible to construct estimators of two quantile residual life functions subject to an order restriction. Such estimators are shown to be strongly uniformly consistent and asymptotically unbiased. We develop the weak convergence theory for these estimators. Simulations seem to indicate that both of the restricted estimators improve on the empirical (unrestricted) estimators in terms of the mean squared error, uniformly at all quantiles, and for a variety of distributions.

本文从分位数剩余寿命的角度研究了混合模型的一些属性。结果表明，混合模型通过分位数剩余寿命受其组成部分的限制。我们研究了混合模型在其组件排序时如何根据分位数剩余寿命函数进行排序。此外，我们证明了混合物的极限分位数剩余寿命与无穷大处的最大组分的剩余寿命相似。基于这些结果，可以构建受阶数限制的两个分位数剩余寿命函数的估计量。这样的估计量被证明是强一致一致且渐近无偏的。我们为这些估计量开发了弱收敛理论。