论文检索

摘要暂缺

一般维修模型的非参数估计AI 解读

The construction and analysis of repair models is an important area in reliability. A commonly used model is the minimal repair model. Under this model, repair restores the state of the system to its level prior to failure. Kijima introduced repair models that could be classified as "better-than-minimal." Under Kijima's models, the system, upon repair, is functionally the same as a working system of lesser age which has never experienced failure. In this paper, we present a…

基于似然比的生存函数置信带AI 解读

Thomas and Grunkemeier introduced a nonparametric likelihood ratio approach to confidence interval estimation of survival probabilities based on right-censored data. We construct simultaneous confidence bands using this approach. The boundaries of the bands are contained within [0, 1]. A procedure essentially equivalent to a bias correction is developed. The resulting increase in coverage accuracy is illustrated by an example and a simulation study. We look at various…

不完整生存数据中分位数函数的非参数似然比置信带AI 解读

The purpose of this paper is to derive confidence bands for quantile functions using a nonparametric likelihood ratio approach. The method is easy to implement and has several appealing properties. It applies to right-censored and left-truncated data, and it does not involve density estimation or even require the existence of a density. Previous approaches (e.g., bootstrap) have imposed smoothness conditions on the density. The performance of the proposed method is…

不完全修复模型中最小修复假设的检验AI 解读

Models assuming minimal repair specify that on repair, a failed system is returned to the working state, while the effective age of the system is held constant; that is, the distribution of the time until the next failure of the repaired system is the same as for a system of the same age that has not yet failed. These models are common in the literature of operations research and reliability, and many probabilistic results as well as inferential procedures depend on the…

不完全修复模型的非参数方法AI 解读

In the age-dependent minimal repair model of Block, Borges and Savits (BBS), a system failing at age $t$ undergoes one of two types of repair. With probability $p(t)$, a perfect repair is performed and the system is returned to the "good-as-new" state, while with probability $1 - p(t)$, a minimal repair is performed and the system is repaired, but is only as good as a working system of age $t$. Whitaker and Samaniego propose an estimator for the system life distribution $F$ w…

随机删失数据的卡方拟合优度检验AI 解读

In this article, procedures analogous to Karl Pearson's well-known chi-squared goodness-of-fit test for a simple null hypothesis are developed under the random censorship model. It is shown that one straightforward analog of Pearson's statistic is diminished in applicability due to the form of its limiting distribution. This leads to the development of an asymptotically exact test based on a Wald-type statistic with a chi-squared limiting null distribution. This test is…

摘要暂缺

摘要暂缺

指数性与平均剩余寿命趋势转折的检验AI 解读

Given that an item is of age $t$, the expected value of the random remaining life is called the mean residual life (MRL) at age $t$. We propose two new nonparametric classes of life distributions for modeling aging based on MRL. The first class of life distributions consists of those with "increasing initially, then decreasing mean residual life" (IDMRL). The IDMRL class models aging that is initially beneficial, then adverse. The second class, "decreasing, then increasing…

用于刻画老化的一类寿命分布AI 解读

We introduce a new better than used of age t 0 (NBU-t 0) class of life distributions, where the survival probability at age 0 is greater than or equal to the conditional survival probability at specified age t 0 > 0. The dual class of new worse than used of age t 0 (NWU-t 0) life distributions is defined by reversing the direction of inequality. Preservation and nonpreservation properties of the two classes under various reliability operations are presented. We also show how…

Ferguson 分布函数贝叶斯估计量的稳健性AI 解读

We derive an explicit expression for the Bayes risk (using weighted squared error loss) of Dalal's Bayes estimator of a symmetric distribution under a $\mathscr{G}$-invariant Dirichlet process prior. We compare this risk to the risk of Ferguson's estimator of an arbitrary distribution under the $\mathscr{G}$-invariant prior. This enables us to (i) assess the savings in risk attained by incorporating known symmetry structure in the model and (ii) provide information about the…

随机删失数据下“新优于旧”寿命性质的检验AI 解读

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…

检验两组评判者之间的排序一致性AI 解读

The ‘problem of m rankings’, so named by M. G. Kendall and studied extensively by Kendall & Babington Smith (1939), Kendall (1970) and others, considers the relationship between the rankings that a group of m judges assigns to a set of k objects. Suppose that there are two groups of judges ranking the objects. Given that there is agreement within each group of judges, how can one test for evidence of agreement between the two groups ? Schucany & Frawley (1973) proposed a…

Dirichlet 先验下的秩次估计AI 解读

Suppose that a sample of size $n$ from a distribution function $F$ is obtained. However, only $r(< n)$ values from the sample are observed, say $X_1,\cdots, X_r$. Without loss of generality, we can consider $X_1,\cdots, X_r$ to be the first $r$ values in the (unordered) sample. The problem is to estimate the rank order $G$ of $X_1$ among $X_1,\cdots, X_n$. The situations of interest include $F$ nonrandom, either known or unknown, and $F$ random. The random case assumes that $F$…

摘要暂缺

分布函数的经验贝叶斯估计AI 解读

A sequence of empirical Bayes estimators is defined for estimating a distribution function. The sequence is shown to be asymptotically optimal relative to a Ferguson Dirichlet process prior. Exact risk expressions are derived and the rate, at which the overall expected loss approaches the minimum Bayes risk, is exhibited. The empirical Bayes approach, based on the Dirichlet process, is also applied to the problem of estimating the mean of a distribution.

摘要暂缺

平均剩余寿命的检验AI 解读

In this paper we develop tests for alternatives representing decreasing mean residual life and the property ‘new better than used in expectation’. The decreasing mean residual life test statistic, V*, is new, and critical constants and a large-sample approximation are obtained to make the test readily applicable. The new better than used in expectation statistic, K*, is shown to be equivalent to the total time on test statistic; the latter is ordinarily viewed as a test…

平均剩余寿命的检验AI 解读

In this paper we develop tests for alternatives representing decreasing mean residual life and the property ‘new better than used in expectation’. The decreasing mean residual life test statistic, V*, is new, and critical constants and a large-sample approximation are obtained to make the test readily applicable. The new better than used in expectation statistic, K*, is shown to be equivalent to the total time on test statistic; the latter is ordinarily viewed as a test…

摘要暂缺

Wilcoxon 检验对某类样本间依赖的稳健性AI 解读

Robustness properties of the two-sample Wilcoxon test are established when the assumption of independence between samples is weakened to allow pairing. In particular, the test is shown to be (asymptotically) conservative when the bivariate distribution governing the pairing is positively quadrant dependent.

摘要暂缺

随机区组设计中针对有序备择的无分布正态分数检验AI 解读

We introduce a normal scores test for ordered alternatives among k treatments in the randomized block design. For k = 2 or 3, the test is equivalent to a standard test due to Page [5]. For k ≥ 4, the test differs from Page's and is often more efficient. As k→ ∞, the Pitman asymptotic relative efficiency of the normal scores test compared to Page's test tends to ∞ for uniform and exponential populations. For normal, uniform and exponential populations, this efficiency exceeds…