Coverage probability

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

Interval estimation of binomial proportion in clinical trials with a two‐stage design

Abstract: Generally, a two-stage design is employed in Phase II clinical trials to avoid giving patients an ineffective drug. If the number of patients with significant improvement, which is a binomial response, is greater than a pre-specified value at the first stage, then another binomial response at the second stage is also observed. This paper considers interval estimation of the response probability when the second stage is allowed to continue. Two asymptotic interval estimators, Wald and score, as well as two exact interval estimators, Clopper-Pearson and Sterne, are constructed according to the two binomial responses from this two-stage design, where the binomial response at the first stage follows a truncated binomial distribution. The mean actual coverage probability and expected interval width are employed to evaluate the performance of these interval estimators. According to the comparison results, the score interval is recommended for both Simon's optimal and minimax designs.

Fundamentals of the Downlink Green Coverage and Energy Efficiency in Heterogeneous Networks

Abstract: This paper studies the proposed green (energy-efficient) coverage probability, link and network energy efficiencies in the downlink of a heterogeneous cellular network (HetNet) consisting of $K$ independent Poisson point processes (PPPs) of base stations (BSs). The important statistical properties of the universal (general) cell association functions are first studied and the cell load statistics for power-law cell association functions, which can characterize the accurate void cell probability of a BS in every tier, is also derived. A simple and feasible green channel-aware cell association (GCA) scheme is proposed and the green coverage probability is also proposed for any particular cell association scheme, such as the maximum received power association (MRPA) and nearest base station association (NBA) schemes. Then the link and network energy efficiencies are proposed to characterize the mean spectrum efficiency per unit power consumption for a BS and the mean area spectrum efficiency for a HetNet, respectively. All the tight bounds on the green coverage probability, link and network energy efficiencies for the GCA, MRPA and NBA schemes are found. They are theoretically shown to pose the fundamental maximum limits on the link and network energy efficiencies achieved by any other cell association schemes and such a fact is validated by numerical results as well.

Coverage Probability and Ergodic Capacity of Intelligent Reflecting Surface-Enhanced Communication Systems

Abstract: This paper studies the performance of a single-input single-output (SISO) system enhanced by the assistance of an intelligent reflecting surface (IRS), which is equipped with a finite number of elements under Rayleigh fading channels. From the instantaneous channel capacity, we compute a closed-form expression of the coverage probability as a function of statistical channel information only. A scaling law of the coverage probability and the number of phase shifts is further obtained. The ergodic capacity is derived, then a simple upper bound to simplify matters of utilizing the symbolic functions and can be applied for a long period of time. Numerical results manifest the tightness and effectiveness of our closed-form expressions compared with Monte-Carlo simulations.

Implementing tests with correct size in the simultaneous equations model

Abstract: In this paper, we propose a “x to the size distortions of tests for struc- tural parameters in the simultaneous equations model by computing critical value functions based on the conditional distribution of test statistics. The conditional tests can then be used to construct informative con“dence regions for the struc- tural parameter with correct coverage probability. Commands to implement these tests in Stata are also introduced. Together with the Anderson…Rubin ( 1949 )a n d score tests, the conditional Wald and likelihood-ratio tests can be used to construct con“dence intervals that have correct coverage probability even when instruments may be weak and that are informative when instruments are good. The regions based on the conditional Wald test necessarily contain the 2SLS estimator, while the ones based on the conditional likelihood-ratio and score tests are centered around the limited-information maximum likelihood (LIML) e stimator. Therefore, con“dence regions based on these tests can be used as reliable evidence of the accuracy of commonly used estimators. In Section 2 ,e x act results are developed for the two-equation model under the assumption that the reduced-form disturbances are normally distributed with a known