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

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Structural Changes and their Econometric Modeling (TES 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 808))

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Abstract

This paper investigates the performance of the confidence intervals for a single inverse mean and the difference of two inverse means of normal distributions with unknown coefficients of variation (CVs). The confidence intervals for the inverse mean with unknown coefficient of variation (CV) were constructed based on the generalized confidence interval (GCI) approach and the large sample approach. The generalized confidence interval and large sample confidence interval for the inverse mean with unknown CV were compared with the generalized confidence interval for the inverse mean of Niwitpong and Wongkhao [5]. Moreover, the confidence intervals for the difference of inverse means with unknown CVs were constructed using the GCI approach, large sample approach and method of variance estimates recovery (MOVER) approach and then compared with existing confidence interval for the difference of inverse means based on the GCI approach of Niwitpong and Wongkhao [6]. The coverage probability and average length of the confidence intervals were evaluated by a Monte Carlo simulation. Carrying out the simulation studies, the results showed that the generalized confidence interval provides the best confidence interval for the inverse mean with unknown CV. The generalized confidence interval and the MOVER confidence interval for the difference of inverse means with unknown CVs perform well in terms of the coverage probability and average length. Finally, two real datasets are analyzed to illustrate the proposed confidence intervals.

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Acknowledgements

This research was funded by King Mongkut’s University of Technology North Bangkok. Contract no. KMUTNB-61-DRIVE-006.

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Authors and Affiliations

  1. Faculty of Applied Science, Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

    Warisa Thangjai, Sa-Aat Niwitpong & Suparat Niwitpong

Authors
  1. Warisa Thangjai
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  2. Sa-Aat Niwitpong
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  3. Suparat Niwitpong
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Corresponding author

Correspondence to Warisa Thangjai .

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Editors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

  2. Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand

    Songsak Sriboonchitta

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Thangjai, W., Niwitpong, SA., Niwitpong, S. (2019). Confidence Intervals for the Inverse Mean and Difference of Inverse Means of Normal Distributions with Unknown Coefficients of Variation. In: Kreinovich, V., Sriboonchitta, S. (eds) Structural Changes and their Econometric Modeling. TES 2019. Studies in Computational Intelligence, vol 808. Springer, Cham. https://doi.org/10.1007/978-3-030-04263-9_19

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