Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation
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 singl...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/5/3/39 |
| _version_ | 1818212796348760064 |
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| author | Warisa Thangjai Suparat Niwitpong Sa-Aat Niwitpong |
| author_facet | Warisa Thangjai Suparat Niwitpong Sa-Aat Niwitpong |
| author_sort | Warisa Thangjai |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T05:54:05Z |
| format | Article |
| id | doaj.art-74071c6fae594bd1a14f095f47f8d749 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-12T05:54:05Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-74071c6fae594bd1a14f095f47f8d7492022-12-22T00:35:36ZengMDPI AGMathematics2227-73902017-07-01533910.3390/math5030039math5030039Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of VariationWarisa Thangjai0Suparat Niwitpong1Sa-Aat Niwitpong2Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology NorthBangkok, Bangkok 10800, ThailandDepartment of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology NorthBangkok, Bangkok 10800, ThailandDepartment of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology NorthBangkok, Bangkok 10800, ThailandThis 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.https://www.mdpi.com/2227-7390/5/3/39meancoefficient of variation (CV)normal distributiongeneralized confidence interval (GCI) approachmethod of variance estimates recovery (MOVER) approach |
| spellingShingle | Warisa Thangjai Suparat Niwitpong Sa-Aat Niwitpong Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation Mathematics mean coefficient of variation (CV) normal distribution generalized confidence interval (GCI) approach method of variance estimates recovery (MOVER) approach |
| title | Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation |
| title_full | Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation |
| title_fullStr | Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation |
| title_full_unstemmed | Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation |
| title_short | Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation |
| title_sort | confidence intervals for mean and difference between means of normal distributions with unknown coefficients of variation |
| topic | mean coefficient of variation (CV) normal distribution generalized confidence interval (GCI) approach method of variance estimates recovery (MOVER) approach |
| url | https://www.mdpi.com/2227-7390/5/3/39 |
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