Testing Whether New is Better than Used with Randomly Censored Data

A life distribution $F$ , with survival function $\bar{F} \equiv 1 - F$ , is new better than used (NBU) if $\bar{F}(x + y) \leq \bar{F}(x)\bar{F}(y)$ for all $x, y \geq 0$ . We propose a test of $H_0 : F$ is exponential, versus $H_1 : F$ is NBU, but not exponential, based on a randomly censored sample of size $n$ from $F$ . Our test statistic is $J^c_n = \int \int \bar{F}_n(x + y) dF_n(x) dF_n(y)$ , where $F_n$ is the Kaplan-Meier estimator. Under mild regularity on the amount of censoring, the asymptotic normality of $J^c_n$ , suitably normalized, is established. Then using a consistent estimator of the null standard deviation of $n^{1/2}J^c_n$ , an asymptotically exact test is obtained. We also study, using tests for the censored and uncensored models, the efficiency loss due to the presence of censoring.A life distribution $F$, with survival function $\bar{F} \equiv 1 - F$, is new better than used (NBU) if $\bar{F}(x + y) \leq \bar{F}(x)\bar{F}(y)$ for all $x, y \geq 0$. We propose a test of $H_0 : F$ is exponential, versus $H_1 : F$ is NBU, but not exponential, based on a randomly censored sample of size $n$ from $F$. Our test statistic is $J^c_n = \int \int \bar{F}_n(x + y) dF_n(x) dF_n(y)$, where $F_n$ is the Kaplan-Meier estimator. Under mild regularity on the amount of censoring, the asymptotic normality of $J^c_n$, suitably normalized, is established. Then using a consistent estimator of the null standard deviation of $n^{1/2}J^c_n$, an asymptotically exact test is obtained. We also study, using tests for the censored and uncensored models, the efficiency loss due to the presence of censoring.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）

笔记与分组

分类依据与纠错

Testing Whether New is Better than Used with Randomly Censored Data

代码、数据与补充材料

随机删失数据下“新优于旧”寿命性质的检验

原文摘要

同方向的基础文献

同方向的基础文献