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379184

A Robust Nonparametric Yeo- Johnson- Transformation- Based Confidence Interval for Quantiles of Skewed Distributions

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Last updated: 24 Dec 2024

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Abstract

The main goal of this paper is to introduce a new robust nonparametric confidence interval for population quantiles. To achieve this goal, a robustified version of an exact equal-tailed two-sided confidence interval for normal quantiles is first introduced. The proposed confidence interval uses the Yeo-Johnson family of power transformations to bring the data into approximate normality or at least symmetry. Calculating the robustified confidence interval using the transformed data then transforming back the lower and upper limits of the confidence interval, the new proposed robust nonparametric confidence interval for population quantile is obtained. Through a simulation study, the proposed confidence interval is evaluated and compared with some competitor existing confidence intervals. The criteria used to evaluate and compare the performance of confidence intervals are: the coverage probability (CP), the mean length of confidence intervals (ML), and the root mean squared deviations of confidence interval's midpoints from the true population quantiles (RMSmdp) of the confidence intervals from the true population quantile. There are no sample size restrictions on the new proposed confidence interval. Simulation results show a significant outperformance of the proposed confidence interval compared to all other competitors under investigation.

DOI

10.21608/acj.2024.379184

Keywords

Robust Estimators, Nonparametric Confidence Intervals, Central and Intermediate Quantiles, Yeo-Johnson Family of Power Transformation, The Bi-weight Location and Scale Estimators, Siddiqui-Bloch-Gastwirth Estimator, Sectioning, Batching, Empirical Likelihood, Kernel Quantile Estimators, Fixed-smoothing Asymptotics

Authors

First Name

Labiba Hassab Elnaby

Last Name

Alatar

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Affiliation

Assistant Professor at Department of Statistics Faculty of Business, Alexandria University

Email

labiba.elatar@alexu.edu.eg

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First Name

Fatma Gaber

Last Name

Abdelaty

MiddleName

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Affiliation

Lecturer at Department of Statistics Faculty of Business, Alexandria University

Email

fatma.gaber@alexu.edu.eg

City

الإسكندرية

Orcid

-

First Name

Mohammad Ibrahim Soliman

Last Name

Gaafar

MiddleName

-

Affiliation

Lecturer at Department of Statistics Faculty of Business, Alexandria University

Email

mohammad.solayman@alexu.edu.eg

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-

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Volume

61

Article Issue

5

Related Issue

50296

Issue Date

2024-09-01

Receive Date

2024-05-29

Publish Date

2024-09-01

Page Start

157

Page End

176

Print ISSN

2682-4183

Online ISSN

2682-4191

Article File

ACJ_Volume 61_Issue 5_Pages 157-176.pdf

PDF . 4.7MB

Link

https://acjalexu.journals.ekb.eg/article_379184.html

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https://acjalexu.journals.ekb.eg/service?article_code=379184

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5

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المقالة الأصلية

Type Code

759

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Journal

Publication Title

مجلة جامعة الإسکندرية للعلوم الإدارية

Publication Link

https://acjalexu.journals.ekb.eg/

MainTitle

A Robust Nonparametric Yeo- Johnson- Transformation- Based Confidence Interval for Quantiles of Skewed Distributions

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Article

Created At

24 Dec 2024