Coverage probability

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

Upper and Lower Bound Distributions That Give Simultaneous Confidence Intervals for Quantiles

Abstract: We propose a new method for constructing parametric confidence intervals for quantiles of an unknown distribution. These confidence intervals are constructed so that the joint probability that all intervals simultaneously contain their respective percentiles is at least a preset value. Thus we may also use the set of either upper or lower confidence limits to define an upper (or lower) bound distribution function, which we call an upper (or lower) tolerance distribution because this distribution may also be used to construct tolerance intervals for the unknown distribution. We derive tolerance distributions with exact coverage probability for iid samples from distributions in the location-scale family. Tolerance distributions can also be used for best- and worst-case analyses, as we illustrate by considering bounds on the distribution of the time interval between the onset of infectiousness and development of detectable antibody in individuals newly infected with the human immunodeficiency virus ...

Estimation of a population size through capture-mark-recapture method: a comparison of various point and interval estimators

Abstract: This article deals with the estimation of a fixed population size through capture-mark-recapture method that gives rise to hypergeometric distribution. There are a few well-known and popular point estimators available in the literature, but no good comprehensive comparison is available about their merits. Apart from the available estimators, an empirical Bayes (EB) estimator of the population size is proposed. We compare all the point estimators in terms of relative bias and relative mean squared error. Next, two new interval estimators – (a) an EB highest posterior distribution interval and (b) a frequentist interval estimator based on a parametric bootstrap method, are proposed. The comparison is then carried among the two proposed interval estimators and interval estimators derived from the currently available estimators in terms of coverage probability and average length (AL). Based on comprehensive numerical results, we rank and recommend the point estimators as well as interval estimators for practi...

Confidence Intervals Based on Rounded Data from the Balanced One-Way Normal Random Effects Model

Abstract: In standard statistical analyses, data are assumed to be essentially exact. But indeed they are often obtained from a relatively crude gaging method and are thus intrinsically “rounded” to some nearest unit. The discussions in Lee and Vardeman (Lee, Chiang-Sheng, Vardeman, Stephen B. (2001). Interval estimation of a normal process mean from rounded data. Journal of Quality Technology 33:335–348.) and Lee and Vardeman (Lee, Chiang-Sheng, Vardeman, Stephen B. (2002). Interval estimation of a normal process standard deviation from rounded data. Communications in Statistics 31:13–34.) for a rounded sample from a single normal distribution established that nominal confidence levels of standard intervals for μ and σ are much larger than actual coverage probabilities when the rounding is severe. In this article we consider interval estimation in the balanced normal one-way random effects model. We demonstrate the deficiency of standard interval estimators in the presence of rounding and show how likelih...

Inferences on the ratio of two generalized variances: independent and correlated cases

Abstract: Statistical inferences about the dispersion of multivariate population are determined by generalized variance. In this article, we consider constructing a confidence interval and testing the hypotheses about the ratio of two independent generalized variances, and the ratio of two dependent generalized variances in two multivariate normal populations. In the case of independence, we first propose a computational approach and then obtain an approximate approach. In the case of dependence, we give an approach using the concepts of generalized confidence interval and generalized p value. In each case, simulation studies are performed for comparing the methods and we find satisfactory results. Practical examples are given for each approach.