Coverage probability

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

Interference and Coverage Analysis for Terahertz Networks With Indoor Blockage Effects and Line-of-Sight Access Point Association

Abstract: Providing high-bandwidth and fast-speed links, wireless local area networks (WLANs) in the Terahertz (THz) band have huge potential for various bandwidth-intensive indoor applications. However, due to the specific phenomena in the THz band, including severe reflection loss, indoor blockage effects, multi-path fading, the analysis on the interference and coverage probability at a downlink is challenging. In this paper, indoor blockage effects caused by the walls and human bodies are analyzed. Next, a statistical THz channel model is proposed to characterize the THz indoor propagation. In light of these, the moment generating functions of the aggregated interference and theoretical expressions for the mean interference power are derived. As a result, the approximated coverage probability and average network throughput are derived. Extensive numerical results show that for the nearest access point (nearest-AP) user association scheme, the optimal AP density is 0.15/m 2, which results in the coverage probability reaches 93% and the average network throughput is 30 Gbps/m 2. In addition, by adopting a novel line-of-sight access point (LoS-AP) user association mechanism, the coverage probability and the average network throughput can be further improved by 3 percent and 2 Gbps/m 2, respectively.

Exact inference for a simple step-stress model from the exponential distribution under time constraint

Abstract: In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress factors such as temperature, voltage and load on the lifetimes of experimental units. Step-stress test, which is a special class of accelerated life-tests, allows the experimenter to increase the stress levels at fixed times during the experiment in order to obtain information on the parameters of the life distributions more quickly than under normal operating conditions. In this paper, we consider the simple step-stress model from the exponential distribution when there is time constraint on the duration of the experiment. We derive the maximum likelihood estimators (MLEs) of the parameters assuming a cumulative exposure model with lifetimes being exponentially distributed. The exact distributions of the MLEs of parameters are obtained through the use of conditional moment generating functions. We also derive confidence intervals for the parameters using these exact distributions, asymptotic distributions of the MLEs and the parametric bootstrap methods, and assess their performance through a Monte Carlo simulation study. Finally, we present two examples to illustrate all the methods of inference discussed here.

The effects of model selection on confidence intervals for the size of a closed population.

Abstract: One encounters in the literature estimates of some rates of genetic and congenital disorders based on log-linear methods to model possible interactions among sources. Often the analyst chooses the simplest model consistent with the data for estimation of the size of a closed population and calculates confidence intervals on the assumption that this simple model is correct. However, despite an apparent excellent fit of the data to such a model, we note here that the resulting confidence intervals may well be misleading in that they can fail to provide an adequate coverage probability. We illustrate this with a simulation for a hypothetical population based on data reported in the literature from three sources. The simulated nominal 95 per cent confidence intervals contained the modelled population size only 30 per cent of the time. Only if external considerations justify the assumption of plausible interactions of sources would use of the simpler model's interval be justified.

On the uniform asymptotic validity of subsampling and the bootstrap

Abstract: This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These results are then applied (i) to construct confidence regions that behave well uniformly over $\mathbf{P}$ in the sense that the coverage probability tends to at least the nominal level uniformly over $\mathbf{P}$ and (ii) to construct tests that behave well uniformly over $\mathbf{P}$ in the sense that the size tends to no greater than the nominal level uniformly over $\mathbf{P}$. Without these stronger notions of convergence, the asymptotic approximations to the coverage probability or size may be poor, even in very large samples. Specific applications include the multivariate mean, testing moment inequalities, multiple testing, the empirical process and $U$-statistics.

Empirical Bayes Confidence Sets for the Mean of a Multivariate Normal Distribution

Abstract: Through the use of an empirical Bayes argument, a confidence set for the mean of a multivariate normal distribution is derived. The set is a recentered sphere, is easy to compute, and has uniformly smaller volume than the usual confidence set. An exact formula for the coverage probability is derived, and numerical evidence is presented which shows that the empirical Bayes set uniformly dominates the usual set in coverage probability.