A Comparison on Confidence Intervals Estimation Methods for the Parameter of Exponential Distribution with Outlier

Abstract

The objective of this research is to compare three methods of estimation confidence intervals forthe parameter of exponential distribution with outlier. The methods are Normal method, Root of QuadraticEquation method, and Bayesian Interval method. The research was considered by the approximateconfidence coefficients and the average width of the confidence intervals. The comparisons were doneby using sample sizes are 20, 40, 100, and 200 whereas parameters θ from 1 to 10 increasing by 1. Thedistributions of outliers have chi-squares and lognormal distribution. The percentages of outlier are 5 and10. All of which are considered at 95% confidence level. This research used the Monte Carlo Simulationmethod. The experiment was repeated 1,000 times for each condition. Results of the research are asfollows:

Normal method, this method meets both requirement of approximate confidence coefficient notlower than given confidence coefficient and the average confidence interval widths are lowest when theparameter θ is 1 in all sample sizes.

Root of Quadratic Equation method, this method meets both requirement of approximateconfidence coefficient not lower than given confidence coefficient and the average confidence intervalwidths are lowest when sample sizes are 100 and 40 whereas the percentages of outlier are 5 and 10,respectively.

Bayesian Interval method, this method meets both requirement of approximate confidencecoefficient not lower than given confidence coefficient and the average confidence interval widths arelowest in two cases. First case, sample sizes are 20, 40, and 100 when the percentage of outlier is 5.Second case, sample sizes are 20, 100, and 200 when the percentage of outlier is 10 in most parametervalues.