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Journal of Applied Sciences
  Year: 2011 | Volume: 11 | Issue: 3 | Page No.: 528-534
DOI: 10.3923/jas.2011.528.534
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Confidence Interval for Locations of Non-kurtosis and Large Kurtosis Leptokurtic Symmetric Distributions

Faris M. Al-Athari

This study shows that the Student’s t confidence interval for the normal distribution is not the right estimator for locations of non-kurtosis and large kurtosis leptokurtic symmetric distributions and proposes three alternative confidence intervals based on robust estimators which are analogous to the Student's t confidence interval. These estimators were tried on 40000 simulated samples of sizes 20(10)50,100 from, three different non-kurtosis, normal and two different large kurtosis leptokurtic, symmetric distributions. These confidence intervals have been studied with regard to both robustness of validity (the error rate) and the robustness of efficiency (the length of the interval) and compared with each other and with Student's t confidence interval by calculating the coverage probability, the average width, the robustness bounds and the margin of error. The best confidence interval has been selected to have the smallest average width within the confidence intervals that have coverage probabilities not less than the lower bound of the robustness. MAD t confidence intervals followed by Sps t are found to be the strongest while Student's t and Downton's t are not preferred at all.
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  •    On Efficient Confidence Intervals for the Log-Normal Mean
  •    Confidence Interval for the Mean of a Contaminated Normal Distribution
How to cite this article:

Faris M. Al-Athari , 2011. Confidence Interval for Locations of Non-kurtosis and Large Kurtosis Leptokurtic Symmetric Distributions. Journal of Applied Sciences, 11: 528-534.

DOI: 10.3923/jas.2011.528.534






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