Estimating Confidence Intervals for Appropriate Binomial Proportional Parameters in Different Situations
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Abstract
The objective of this research is to compare the performance of 95% interval estimation methods for binomial proportional parameters, namely the adjusted Wald method, the Geoffrey method, the Zhou-Li method, and the Kim-Jang method, using the criteria. Used to measure efficiency is to check the confidence coefficient at the 95% level and compare the average width of the confidence interval. Data were modeled using Monte Carlo techniques to have a binomial distribution with parameters n equal to 10, 20, 30, 70, 90, 100, 200, 500 and 1000 and p equal to 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9. A total of 81 situations were studied. The experiment was repeated 5000 times for each scenario. The research results found that The Geoffrey method performs well at almost all sample size levels and at almost all p parameters, except when the sample size is small and the p parameter approaches 0.5. The adaptive Wald method performs well. At all levels of sample size and p parameters ranging from 0.3 to 0.7, the Zhou-Li method has good performance. at all sample sizes and at almost all p parameters, except in the case where the sample size is equal to 10 at all p parameters. In addition, the Kim-Jang method performs well at almost all sample sizes and at almost all p parameters, except in the case of small sample sizes and where the parameters are Values 0.1 and 0.9
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