Confidence Interval for the Inverse of a Normal Mean with a Known Coefficient of Variation

Authors: Arunee Wongkha, Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.

Keywords: The inverse of a normal mean, confidence interval, generalized confidence intervals, known coefficient of variation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087796

References:

[1] E. Lamanna, G. Romano and C. Sgrbi, “Curvature measurements in nuclear emulsions,” Nuclear Instruments and Methods, vol. 187, pp. 387-391, 1981.
[2] A. Zaman, “Estimates without moments: the case of the reciprocal of a normal mean,” Journal of Econometrics, vol. 15, pp. 289-298, 1981a.
[3] A. Zaman, “A complete class theorem for the control problem and the future results on admissibility and inadmissibility,” Annals of Statistics, vol. 9, pp. 812-821, 1981b.
[4] C. S. withers and S. Nadarajah, “Estimators for the inverse powers of a normal mean,” Journal of Statistical Planning and Inference, vol. 143, pp. 441-455, 2013.
[5] S. Weerahandi, “Generalized confidence intervals,” Journal of the American Statistical Association, vol. 88, no. 423, pp. 899-905, Sep. 1993.
[6] R. Mahmoudvand and H. Hassani, “Two new confidence intervals for the coefficient of variation in a normal distribution,” Journal of Applied Statistics, vol. 36, no. 4, pp. 429-442, 2009.