780 research outputs found

    Tolerance and confidence limits for classes of distributions based on failure rate

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    Tolerance and confidence limits for classes of distributions based on failure rate

    Estimation of Conditional Power for Cluster-Randomized Trials with Interval-Censored Endpoints

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    Cluster-randomized trials (CRTs) of infectious disease preventions often yield correlated, interval-censored data: dependencies may exist between observations from the same cluster, and event occurrence may be assessed only at intermittent clinic visits. This data structure must be accounted for when conducting interim monitoring and futility assessment for CRTs. In this article, we propose a flexible framework for conditional power estimation when outcomes are correlated and interval-censored. Under the assumption that the survival times follow a shared frailty model, we first characterize the correspondence between the marginal and cluster-conditional survival functions, and then use this relationship to semiparametrically estimate the cluster-specific survival distributions from the available interim data. We incorporate assumptions about changes to the event process over the remainder of the trial---as well as estimates of the dependency among observations in the same cluster---to extend these survival curves through the end of the study. Based on these projected survival functions we generate correlated interval-censored observations, and then calculate the conditional power as the proportion of times (across multiple full-data generation steps) that the null hypothesis of no treatment effect is rejected. We evaluate the performance of the proposed method through extensive simulation studies, and illustrate its use on a large cluster-randomized HIV prevention trial

    A partial ordering of rank densities

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    AbstractA function f(π) on the set of permutations of {1, 2, …, n} is called arrangement increasing (AI) if it increases each time we transpose a pair of coordinates in descending order, i < j and πi > πj, putting them in ascending order. We define and develop a partial ordering ≤AI on densities of rank vectors in terms of expectations of AI functions. Specially, one density g is defined to be AI-larger than another density f(f≤AI g) if the expectation under g of any AI function is at least as large as its expectation under f. We show that the uniform density is the AI-smallest AI density, and this leads to power results for tests of agreement of two rank vectors. The extreme points of the convex set of AI densities are determined, from which additional results concerning the minimum power of rank tests are shown to follow. We also give applications to ranking and selection problems

    A Generalization of the Exponential-Poisson Distribution

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    The two-parameter distribution known as exponential-Poisson (EP) distribution, which has decreasing failure rate, was introduced by Kus (2007). In this paper we generalize the EP distribution and show that the failure rate of the new distribution can be decreasing or increasing. The failure rate can also be upside-down bathtub shaped. A comprehensive mathematical treatment of the new distribution is provided. We provide closed-form expressions for the density, cumulative distribution, survival and failure rate functions; we also obtain the density of the iith order statistic. We derive the rrth raw moment of the new distribution and also the moments of order statistics. Moreover, we discuss estimation by maximum likelihood and obtain an expression for Fisher's information matrix. Furthermore, expressions for the R\'enyi and Shannon entropies are given and estimation of the stress-strength parameter is discussed. Applications using two real data sets are presented

    Statistical Estimation Procedures for the ''burn-in'' Process

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    Statistical estimation procedures for identifying and eliminating poor quality or defective item

    On the Decreasing Failure Rate property for general counting process. Results based on conditional interarrival times

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    In the present paper we consider general counting processes stopped at a random time TT, independent of the process. Provided that TT has the decreasing failure rate (DFR) property, we give sufficient conditions on the arrival times so that the number of events occurring before TT preserves the DFR property of TT. These conditions involve the study of the conditional interarrival times. As a main application, we prove the DFR property in a context of maintenance models in reliability, by the consideration of Kijima type I virtual age models under quite general assumptions
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