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### A robust Condence Interval Based on Modied Trimmed Standard Deviation for the Mean of Positively Skewed Populations

#### Abstract

In this study, we propose a robust confidence interval for the mean of skewed populations. It is simple adjustment of the Student-t confidence interval based on the trimmed mean and the modified trimmed standard deviation. The proposed confidence interval is compared with existing confidence intervals in terms of coverage probability and average width for normal and skewed distributions with different parameter and skewness. The simulation study shows that the proposed robust confidence interval performs the best among the compared confidence intervals and it is better than the classical Student-t confidence interval. Also, proposed confidence interval has narrowest average width in all sample sizes. In addition to the simulation,some real-life examples have been considered for illustrating which support the findings of the simulation study. Consequently, we recommend confidence interval based on trimmed mean and the modified trimmed standard deviation to estimate the mean of positively skewed populations.

DOI Code: 10.1285/i20705948v13n1p164

Keywords: average width; confidence interval; coverage probability; modified trimmed standard deviation; trimmed mean

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