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Constructing a confidence interval for the ratio of normal distribution quantiles

Author

Listed:
  • Malekzadeh Ahad

    (Department of Computer Science and Statistics, Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16765-3381, Tehran, Iran)

  • Mahmoudi Seyed Mahdi

    (Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box 35195-363, Semnan, Iran)

Abstract

In this paper, to construct a confidence interval (general and shortest) for quantiles of normal distribution in one population, we present a pivotal quantity that has non-central t distribution. In the case of two independent normal populations, we propose a confidence interval for the ratio of quantiles based on the generalized pivotal quantity, and we introduce a simple method for extracting its percentiles, based on which a shorter confidence interval can be created. Also, we provide general and shorter confidence intervals using the method of variance estimate recovery. The performance of five proposed methods will be examined by using simulation and examples.

Suggested Citation

  • Malekzadeh Ahad & Mahmoudi Seyed Mahdi, 2020. "Constructing a confidence interval for the ratio of normal distribution quantiles," Monte Carlo Methods and Applications, De Gruyter, vol. 26(4), pages 325-334, December.
    • Handle: RePEc:bpj:mcmeap:v:26:y:2020:i:4:p:325-334:n:1
    DOI: 10.1515/mcma-2020-2070
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    References listed on IDEAS

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    1. Li-Fei Huang, 2017. "Approximated non parametric confidence regions for the ratio of two percentiles," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(8), pages 4004-4015, April.
    2. Zou, Guang Yong & Taleban, Julia & Huo, Cindy Y., 2009. "Confidence interval estimation for lognormal data with application to health economics," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3755-3764, September.
    3. Chakraborti, S. & Li, J., 2007. "Confidence Interval Estimation of a Normal Percentile," The American Statistician, American Statistical Association, vol. 61, pages 331-336, November.
    4. Ahad Malekzadeh & Mahmood Kharrati-Kopaei, 2019. "Inferences on the common mean of several heterogeneous log-normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(6), pages 1066-1083, April.
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