The Confidence Interval of Variance by Adjusted Bonett-t with the Geometric Mean Method for Non-normal Distributions
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Abstract
The objectives of this research were 1) to develop a confidence interval for the one-population variance for non-normal distribution data and 2) to study the efficiency of the confidence interval developed for non-normal distribution data. The simulation was implemented by using 50,000 Monte Carlo random samples of a given sample size from various non-normal distributions (Chi-square, Exponential, Gamma, and Weibull). There were 3 methods for estimating the confidence interval of variance for the one-population variance of non-normal distribution data: 1) Bonet's method, 2) The adjusted Bonett-t with the Median method, and 3) The adjusting Bonett-t with the geometric mean method. The performance considerations of the confidence interval consisted of coverage probability and average length. The results showed that when the sample size was small and the data were not normally distributed, the adjusted Bonett-t with the geometric mean method performed better than the other methods.
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