Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.

Families of smooth confidence bands for the survival function under the general random censorship model

Abstract: Randomly right censored data often arise in industrial life testing and clinical trials. Several authors have proposed asymptotic confidence bands for the survival function when data are randomly censored on the right. All of these bands are based on the empirical estimator of the survival function. In this paper, families of asymptotic (1-α)100% level confidence bands are developed from the smoothed estimate of the survival function under the general random censorship model. The new bands are compared to empirical bands, and it is shown that for small sample sizes, the smooth bands have a higher coverage probability than the empirical counterparts.

The Ginibre Point Process as a Model for Wireless Networks with Repulsion

Abstract: The spatial structure of transmitters in wireless networks plays a key role in evaluating the mutual interference and hence the performance. Although the Poisson point process (PPP) has been widely used to model the spatial configuration of wireless networks, it is not suitable for networks with repulsion. The Ginibre point process (GPP) is one of the main examples of determinantal point processes that can be used to model random phenomena where repulsion is observed. Considering the accuracy, tractability and practicability tradeoffs, we introduce and promote the $\beta$-GPP, an intermediate class between the PPP and the GPP, as a model for wireless networks when the nodes exhibit repulsion. To show that the model leads to analytically tractable results in several cases of interest, we derive the mean and variance of the interference using two different approaches: the Palm measure approach and the reduced second moment approach, and then provide approximations of the interference distribution by three known probability density functions. Besides, to show that the model is relevant for cellular systems, we derive the coverage probability of the typical user and also find that the fitted $\beta$-GPP can closely model the deployment of actual base stations in terms of the coverage probability and other statistics.

Spline-based procedures for dose-finding studies with active control

Abstract: In a dose-finding study with an active control, several doses of a new drug are compared with an established drug (the so-called active control). One goal of such studies is to characterize the dose–response relationship and to find the smallest target dose concentration d*, which leads to the same efficacy as the active control. For this purpose, the intersection point of the mean dose–response function with the expected efficacy of the active control has to be estimated. The focus of this paper is a cubic spline-based method for deriving an estimator of the target dose without assuming a specific dose–response function. Furthermore, the construction of a spline-based bootstrap CI is described. Estimator and CI are compared with other flexible and parametric methods such as linear spline interpolation as well as maximum likelihood regression in simulation studies motivated by a real clinical trial. Also, design considerations for the cubic spline approach with focus on bias minimization are presented. Although the spline-based point estimator can be biased, designs can be chosen to minimize and reasonably limit the maximum absolute bias. Furthermore, the coverage probability of the cubic spline approach is satisfactory, especially for bias minimal designs. © 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Simultaneous inference for several quantiles of a normal population with applications

Abstract: A common statistical problem is to make inference about the mean of a normally distributed population. While the mean and the variance are important quantities, many real problems require information on certain quantiles of the population which combine both the mean and variance. Motivated by two recent applications, we consider simultaneous inference for more than one quantile of interest. In this paper, a set of exact 1-α level simultaneous confidence intervals for several quantiles of a normally distributed population is constructed, based on a simple random sample from that population. The critical constants for achieving an exact 1-α simultaneous coverage probability can be computed efficiently using numerical quadrature involving only a one-dimensional integral combined with standard search algorithms. The proposed methods are illustrated with an example. Several further research problems are identified.

On the Ratio of Exponential and Generalized Gamma Random Variables with Applications to Ad Hoc SISO Networks

Abstract: A Poisson point process (PPP)-based model for a single-input single-output (SISO) transmission between two randomly located nodes is developed and analyzed. The power received at a node, when a randomly deployed transmitter transmits the message signal in the presence of Rayleigh fading and path loss, is shown to be the ratio of an exponential random variable (RV) and a generalized gamma (GG) RV. The cumulative distribution function (CDF) of the received power is derived, which is used to find the outage probability at the receiver. The study is then further extended to SISO multi-hop links where the coverage probability of the network is calculated. Finally, a transmission model is proposed that saves a significant amount of energy by carefully selecting an intermediate node in a multi-hop network such that the lifetime of the network can be increased. Numerical simulations are presented to validate the theoretical models.