**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31821

##### Coverage Probability of Confidence Intervals for the Normal Mean and Variance with Restricted Parameter Space

**Authors:**
Sa-aat Niwitpong

**Abstract:**

Recent articles have addressed the problem to construct the confidence intervals for the mean of a normal distribution where the parameter space is restricted, see for example Wang [Confidence intervals for the mean of a normal distribution with restricted parameter space. Journal of Statistical Computation and Simulation, Vol. 78, No. 9, 2008, 829–841.], we derived, in this paper, analytic expressions of the coverage probability and the expected length of confidence interval for the normal mean when the whole parameter space is bounded. We also construct the confidence interval for the normal variance with restricted parameter for the first time and its coverage probability and expected length are also mathematically derived. As a result, one can use these criteria to assess the confidence interval for the normal mean and variance when the parameter space is restricted without the back up from simulation experiments.

**Keywords:**
Confidence interval,
coverage probability,
expected length,
restricted parameter space.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1072098

**References:**

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[4] H. Wang, Confidence intervals for the mean of a normal distribution with restricted parameter space, Journal of Statistical Computation and Simulation, 78(9) (2008) 829-841.

[5] Wang, H., Modified P-value of two-sided test for normal distribution with restricted parameter space, Communication of Statistics Theory and Method, 35 (2006) 1-14.

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[7] S. Niwitpong, Sa. Niwitpong, Confidence interval for the difference of two normal population means with a known ratio of variances, Applied Mathematical Sciences, 4(8) (2010) 347 - 359.