Upper bound Clopper-Pearson one-sided 95% confidence intervals for an observed Leishmania prevalence of 0%, evaluated by two strata: rodent species (for those species with ≥15 individuals represented) and study site (original) (raw)
Related papers
2014
This study is considered a number of popular confidence interval for binomial proportion and the difference of two binomial proportions . A new approach is proposed base on Bayesian view for binomial proportion and also for difference of two binomial proportions . The Bayes confidence intervals compared with other confidence intervals of coverage probability and expected length . Based on this analysis , and t he simulation study recommend the Bayes confidence interval of binomial proportion and difference of two binomial proportions for small sample , and show their superior performance from both criteria .
A Coverage Probability Approach to Finding an Optimal Binomial Confidence Procedure
The American Statistician, 2014
The problem of finding confidence intervals for the success parameter of a binomial experiment has a long history, and a myriad of procedures have been developed. Most exploit the duality between hypothesis testing and confidence regions and are typically based on large sample approximations. We instead employ a direct approach that attempts to determine the optimal coverage probability function a binomial confidence procedure can have from the exact underlying binomial distributions, which in turn defines the associated procedure. We show that a graphical perspective provides much insight into the problem. Both procedures whose coverage never falls below the declared confidence level and those that achieve that level only approximately are analyzed. We introduce the Length/Coverage Optimal method, a variant of Sterne's procedure that minimizes average length while maximizing coverage among all length minimizing procedures, and show that it is superior in important ways to existing procedures.
Improved Confidence Intervals for the Bernoulli Parameter
2000
Despite the simplicity of the Bernoulli process, developing good confidence-interval procedures for its parameter— the probability of success p—is deceptively difficult. The binary data yield a discrete number of successes from a discrete number of trials, n. This discreteness results in actual coverage probabilities that oscillate with the n for fixed values of p (and with p for fixed n).
Modified Clopper-Pearson Confidence Interval for Binomial Proportion
Journal of Statistical Theory and Applications, 2014
We introduce expected coverage probability as a measure for constructing confidence intervals for the binomial proportion, π. We propose a model based confidence interval for π using the expected coverage probabilities of the Clopper-Pearson interval. The method provides intervals comparable or better than the alternative intervals, such as the Wilson, Agresti-Coull and Jeffreys intervals.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about In the computation of two-sided confidence intervals for the binomial parameter p (using the binomial mass function), it is known that such intervals achieve a confidence coefficient that in general is not equal to the confidence level 1-a, say. In this article we present some general results on the confidence coefficient and tabulate them for selected pairs (c, n = number of trials). We treat only the nominal equal tail probability case because it is the most commonly taught and used.
A Simulated Data Analysis on the Interval Estimation for the Binomial Proportion P
Journal of Educational Policy and Entrepreneurial Research, 2014
This study constructed a quadratic-based interval estimator for binomial proportion p. The modified method imposed a continuity correction over the confidence interval. This modified quadratic-based interval was compared to the different existing alternative intervals through numerical analysis using the following criteria: coverage probability, and expected width for various values of n, p and α = 0.05. Simulated data results generated the following observations: (1) the coverage probability of modified interval is larger compared to that of the standard and non-modified intervals, for any p and n; (2) the coverage probability of all the alternative methods approaches to the nominal 95% confidence level as n increases for any p;(3) the modified and non-modified intervals have indistinguishable width differences for any p as n gets larger; (4) the expected width of the modified and alternative intervals decreases as n increases for 05. 0 and any p. Based on these observations one can say that the modified method is an improvement of the standard method. It is therefore recommended to modify other existing alternative methods in such a way that there's an increase in performance in terms of coverage properties, expected width, and other measures.
A basic statistical problem: Confidence interval for the Bernoulli parameter
Computational Statistics & Data Analysis, 1985
The best methods for setting a confidence interval (CI) for the Bernoulli parameter ~r are presented in a unified way. These methods are compared from many different points of view. Based on this comparison a practical procedure for obtaining a CI for ~r is proposed.
Bayesian Sample Size calculations for binomial experiments
1997
This paper proposes new methodology for calculating the optimal sample size when a hypothesis test between two binomial proportions is conducted. The problem is addressed from the Bayesian point of view. Following the formulation by DasGupta and Vidakovic (1997, J. Statist. Plann. Inference 65, 335-347), the posterior risk is determined and set not to exceed a prespeciÿed bound. A second constraint deals with the likelihood of data not satisfying the bound on the risk. The cases when the two proportions are equal to a ÿxed or to a random value are examined.