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Confidence Intervals for the Difference and Ratio of Medians of the Delta-Lognormal Distribution

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Abstract

The primary objective of this research is to investigate the construction of confidence intervals (CIs) for the difference and ratio of medians, specifically focusing on the delta-lognormal distribution. The study presents five different CI methods: the generalized confidence interval (GCI), the fiducial generalized confidence interval (FGCI), the method of variance estimates recovery (MOVER), the highest posterior density based on Jeffreys prior (H–Jef), and the Jeffreys rule prior (H–JRul). To assess their performance, we compare coverage probabilities and expected lengths obtained through Monte Carlo simulations. The simulation results demonstrate that the H–Jef interval is effective for estimating the median difference, while the H–JRul interval yields the best results for estimating the median ratio. Finally, all the proposed methods are applied to analyze a dataset of daily rainfall data from Mae Hong Son and Nan Meteorological Stations in Thailand.

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Funding

This research has received funding support from the National Science, Research and Innovation Fund (NSRF), and King Mongkut’s University of Technology North Bangkok: KMUTNB-FF-67-B-14.

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Authors and Affiliations

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

    Usanee Janthasuwan, Sa-Aat Niwitpong & Suparat Niwitpong

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  1. Usanee Janthasuwan
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  2. Sa-Aat Niwitpong
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  3. Suparat Niwitpong
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Correspondence to Usanee Janthasuwan, Sa-Aat Niwitpong or Suparat Niwitpong.

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Janthasuwan, U., Niwitpong, SA. & Niwitpong, S. Confidence Intervals for the Difference and Ratio of Medians of the Delta-Lognormal Distribution. Lobachevskii J Math 44, 4717–4732 (2023). https://doi.org/10.1134/S1995080223110185

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  • DOI: https://doi.org/10.1134/S1995080223110185

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