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Profile Likelihood-Based Confidence Interval for the Standard Deviation of the Two-Parameter Exponential Distribution

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Abstract

This paper introduces the novel score function derived using the profile likelihood method to construct the new confidence interval for the standard deviation in the two-parameter exponential distribution. We investigate the performance of the proposed confidence interval using simulations. The results show that the profile likelihood confidence interval performs very well in terms of coverage probability and expected length, and outperforms the standard methods. We also show that the new pivotal quantity obtained from the score function based on the profile likelihood had an approximate standard normal distribution, supported by statistical theory. The confidence interval is illustrated with two datasets on time at failure for a fleet of backhoes in the United States and times between system failures, to confirm simulation results.

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Funding

The author gratefully acknowledge the financial support provided by Faculty of Science and Technology, Thammasat University, Contract no. SciGR5/2563.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, 12120, Pathum Thani, Thailand

    P. Sangnawakij

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  1. P. Sangnawakij
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Correspondence to P. Sangnawakij.

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(Submitted by A. I. Volodin)

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Sangnawakij, P. Profile Likelihood-Based Confidence Interval for the Standard Deviation of the Two-Parameter Exponential Distribution. Lobachevskii J Math 43, 2274–2285 (2022). https://doi.org/10.1134/S1995080222110269

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  • DOI: https://doi.org/10.1134/S1995080222110269

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