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Mathematics 2017, 5(3), 39; doi:10.3390/math5030039

Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation

Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology NorthBangkok, Bangkok 10800, Thailand
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Received: 15 June 2017 / Revised: 24 July 2017 / Accepted: 25 July 2017 / Published: 28 July 2017
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Abstract

This paper proposes confidence intervals for a single mean and difference of two means of normal distributions with unknown coefficients of variation (CVs). The generalized confidence interval (GCI) approach and large sample (LS) approach were proposed to construct confidence intervals for the single normal mean with unknown CV. These confidence intervals were compared with existing confidence interval for the single normal mean based on the Student’s t-distribution (small sample size case) and the z-distribution (large sample size case). Furthermore, the confidence intervals for the difference between two normal means with unknown CVs were constructed based on the GCI approach, the method of variance estimates recovery (MOVER) approach and the LS approach and then compared with the Welch–Satterthwaite (WS) approach. The coverage probability and average length of the proposed confidence intervals were evaluated via Monte Carlo simulation. The results indicated that the GCIs for the single normal mean and the difference of two normal means with unknown CVs are better than the other confidence intervals. Finally, three datasets are given to illustrate the proposed confidence intervals. View Full-Text
Keywords: mean; coefficient of variation (CV); normal distribution; generalized confidence interval (GCI) approach; method of variance estimates recovery (MOVER) approach mean; coefficient of variation (CV); normal distribution; generalized confidence interval (GCI) approach; method of variance estimates recovery (MOVER) approach
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Thangjai, W.; Niwitpong, S.; Niwitpong, S.-A. Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation. Mathematics 2017, 5, 39.

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