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http://dx.doi.org/10.5351/KJAS.2005.18.3.607

Interval Estimation for a Binomial Proportion Based on Weighted Polya Posterior  

Lee Seung-Chun (Department of Statistics, Hanshin University)
Publication Information
The Korean Journal of Applied Statistics / v.18, no.3, 2005 , pp. 607-615 More about this Journal
Abstract
Recently the interval estimation of a binomial proportion is revisited in various literatures. This is mainly due to the erratic behavior of the coverage probability of the will-known Wald confidence interval. Various alternatives have been proposed. Among them, Agresti-Coull confidence interval has been recommended by Brown et al. (2001) with other confidence intervals for large sample, say n $\ge$ 40. On the other hand, a noninformative Bayesian approach called Polya posterior often produces statistics with good frequentist's properties. In this note, an interval estimator is developed using weighted Polya posterior. The resulting interval estimator is essentially the Agresti-Coull confidence interval with some improved features. It is shown that the weighted Polys posterior produce an effective interval estimator for small sample size and a severely skewed binomial distribution.
Keywords
Binomial Proportion; Weighted Polys posterior; Wald interval; Agresti-Coull interval; Wilson interval;
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  • Reference
1 Ghosh, B. K. (1979). A comparison of some approximate confidence intervals for the binomial parameter, Journal of the American Statistical Association, 74, 894-900   DOI   ScienceOn
2 Ghosh, M. and Meeden, G. D. (1998). Bayesian Methods for Finite Population Sampling, Chapman & Hall, London
3 Meeden, G. D. (1999). Interval estimators for the population mean for skewed distributions with a small sample size, Journal of Applied Statistics, 26, 81-96   DOI   ScienceOn
4 Wilson, E. B. (1927). Probable inference, the law of succession and statistical inference, Journal of the American Statistical Association, 22, 209-212   DOI   ScienceOn
5 Agresti, A. and Coull, B. A. (1998). Approximation is better than 'exact' for interval estimation of binomial proportions, American Statistician, 52, 119-126   DOI   ScienceOn
6 Brown, L. D., Cai, T. T. and DasGupta, A. (2002). Confidence intervals for a binomial proportion and asymptotic expansions, The Annals of Statistics, 30, 160-201   DOI   ScienceOn
7 Agresti, A. and Caffo, B. (2000). Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures, The American Statistician, 54, 280-288   DOI   ScienceOn
8 Blyth, C. R. and Still, H. A. (1983). Binomial confidence intervals, Journal of the American Statistical Association, 78, 108-116   DOI   ScienceOn
9 Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion, Statistical Science, 16, 101 - 133
10 Feller, W. (1968). An Introduction of Probability Theory and Its Applications, volumn I, Wiley, New York