Confidence Intervals for the Normal Mean With Known Coefficient of Variation

Niwitpong, Suparat

doi:10.17654/fjmsjul2015_711_727

Cited by 6 publications

(9 citation statements)

References 7 publications

(10 reference statements)

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“…The dataset, previously considered by Niwitpong [9], is fitted by the normal distribution. The data shows the cholesterol level of 15 participants who were given eight weeks of training to truly reduce the cholesterol level.…”

Section: Examplementioning

confidence: 99%

“…Niwitpong et al [6] provided confidence intervals for the difference between normal population means with known CVs. Niwitpong [7] presented confidence intervals for the normal mean with known CV. Niwitpong and Niwitpong [8] proposed the confidence interval for the normal mean with a known CV based on the best unbiased estimator, which was proposed by Khan [3].…”

Section: Introductionmentioning

confidence: 99%

“…Niwitpong [7] presented confidence intervals for the normal mean with known CV. Niwitpong and Niwitpong [8] proposed the confidence interval for the normal mean with a known CV based on the best unbiased estimator, which was proposed by Khan [3]. Niwitpong [9] proposed the confidence interval for the normal mean with a known CV based on the t-test.…”

Section: Introductionmentioning

confidence: 99%

“…Niwitpong and Niwitpong [8] proposed the confidence interval for the normal mean with a known CV based on the best unbiased estimator, which was proposed by Khan [3]. Niwitpong [9] proposed the confidence interval for the normal mean with a known CV based on the t-test. Niwitpong and Niwitpong [10] constructed new confidence intervals for the difference between normal means with known CV.…”

Section: Introductionmentioning

confidence: 99%

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

Thangjai

Niwitpong

2017

Mathematics

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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.

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Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Thangjai

Niwitpong

2017

Mathematics

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“…For example, in environmental studies, inference about the mean of the pollutant is of special interest. And in those studies, the standard deviation of a pollutant is often assumed to be directly related to the mean of the pollutant (Niwitpong [1]). In agricultural studies, it is customary to conduct multi-location trials.…”

Section: Introductionmentioning

confidence: 99%

Inference for the Normal Mean with Known Coefficient of Variation

Fu¹,

Wang²

2013

OJS

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Inference for the mean of a normal distribution with known coefficient of variation is of special theoretical interest because the model belongs to the curved exponential family with a scalar parameter of interest and a two-dimensional minimal sufficient statistic. Therefore, standard inferential methods cannot be directly applied to this problem. It is also of practical interest because this problem arises naturally in many environmental and agriculture studies. In this paper we proposed a modified signed log likelihood ratio method to obtain inference for the normal mean with known coefficient of variation. Simulation studies show the remarkable accuracy of the proposed method even for sample size as small as 2. Moreover, a new point estimator for the mean can be derived from the proposed method. Simulation studies show that new point estimator is more efficient than most of the existing estimators.

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Confidence intervals for the difference between normal means with known coefficients of variation

Niwitpong

2016

Ann Oper Res

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Confidence Intervals for the Normal Mean With Known Coefficient of Variation

Cited by 6 publications

References 7 publications

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

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

Inference for the Normal Mean with Known Coefficient of Variation

Confidence intervals for the difference between normal means with known coefficients of variation

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