Perbandingan Metode Dalil Limit Pusat Transformasi dan Resampling Bootstrap dalam Pembentukan Selang Kepercayaan

Abstract

YULI EKA PUTRI. A Comparative Study of Central Limit Theorem, Transformation and Bootstrap Resampling in Determining Confidence Interval. Supervised by KUSMAN SADIK and CICI SUHAENI.

The confidence interval is usually established under normality assumption. But, many real-life data does not belong to normal distribution. Many of them are skewed, such as chi-square distribution, generalized extreme value (GEV) or other distribution. For such data, we can use central limit theorem, transformation and bootstrap resampling method to construct confidence intervals. The performance of the methods in constructing the interval can be evaluated using confidence interval accuracy value, interval width, and standard deviation of the interval width. Thus we can determine the best method. The method is determined for having better performance if it has higher accuracy value, smaller interval width, and smaller standard deviation of interval width.This research use both simulated and real-life data. Simulated data is generated from the chi-square distribution, GEV and modified non-normal distribution. The modified non-normal distributed data is a modification of normal distributed data using quadratic and logaritm transformation. So that the data is no longer normally distributed. The results show that transformation method is well used for small sample sizes. Bootstrap resampling dan central limit theorem are better used for large sample sizes.