Adjusted Bonett Confidence Interval for Standard Deviation of Non-normal Distributions

Bonett [1] provides an approximate confidence interval for sigma and shows it to be nearly exact under normality and, for small samples, under moderate non-normality. This paper proposes a new method for determining the confidence interval for sigma. We follow the suggestion of Bonett [1] and include any prior kurtosis information. An important modification from the Bonett method is to base the interval on t(alpha/2), the (alpha/2)100th quantile of Student T distribution, rather than on Z(alpha/2), the (alpha/2)100th quantile of standard normal distribution. Further, the use of the median as an estimate of the population mean gives a slightly higher coverage probability for the confidence interval for sigma when data are from skewed leptokurtic distributions. Monte Carlo Simulation results for selected normal and non-normal distributions show that the confidence intervals obtained from the new method have appreciably higher coverage probabilities than the confidence intervals from the original Bonett method that does not use prior kurtosis information, and also higher coverage probabilities than the Bonett method that does use prior kurtosis information.