Alternative Confidence Interval for Variability Parameters in the Normal Distribution with Applications to Stock Exchange Index Data Set

Abstract

This work focusses on estimation the standard deviation (SD) and coefficient of variation (CV) in the normal distribution. These two measures are useful in applications and widely used to report the spread or variability of continuous data. We develop the confidence intervals for these parameters using the two pivotal quantity methods with the unbiased estimator of SD. The first confidence interval uses the pivot function based on a chi-square distribution and the second one is based on a generalized pivotal quantity. The performance of our approaches is conducted via simulations. We show that the confidence intervals for SD and CV based on the new pivots have coverage probabilities greater than existing confidence intervals. Furthermore, they have acceptable short expected lengths. We also provide two real-data sets on the SET50 index of Thailand to demonstrate the proposed methods.