Constructing a confidence interval for the ratio of normal distribution quantiles

Malekzadeh Ahad () and Mahmoudi Seyed Mahdi ()
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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

Monte Carlo Methods and Applications, 2020, vol. 26, issue 4, 325-334

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.

Keywords: Normal distribution; coverage probability; quantiles; confidence interval; generalized pivotal quantity; shortest confidence interval (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/mcma-2020-2070

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