A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS

Ahmed Salih; Arkan Jebur Al-Majidi

A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS

Abstract

Bounded response variables are common in disciplines such as dependability, finance, environmental sciences, and biostatistics, where traditional regression models based on the conditional mean may fail to capture varied covariate effects throughout the response distribution. To solve this issue, this work proposes a flexible quantile regression model based on the Unit Chen distribution for evaluating continuous data on the unit intervals. The proposed methodology defines the conditional quantile via a logit link function, allowing explanatory factors to impact diverse parts of the answer distribution while maintaining limited support. Maximum likelihood estimation is created for the inference of parameters, and the appropriate estimation approach is executed by means of numerical optimization techniques. A number of model diagnostic techniques are included to check the adequacy and robustness of the model, to detect influential data and to examine the sensitivity of the fitted model, including generalized Cook’s distance, likelihood displacement and local influence analysis. The finite-sample performance of the suggested estimators is examined via a comprehensive Monte Carlo simulation analysis employing bias, mean squared error and root mean squared error as assessment measures for varying sample sizes and quantile levels. The practical applicability of the proposed model is illustrated using a real bounded-response dataset and is compared with several competing unit quantile regression models using information criteria and diagnostic measures. The empirical findings demonstrate that the proposed Unit Chen quantile regression model provides accurate parameter estimation, effective diagnostic performance, and competitive model fitting, making it a valuable alternative for modeling bounded response data exhibiting heterogeneous distributional characteristics.

Keywords

References

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Details

Primary Language

English

Subjects

Applied Statistics, Statistics (Other)

Journal Section

Research Article

Authors

Ahmed Salih ^*
0000-0002-6109-224X
Iraq

Arkan Jebur Al-Majidi This is me
0009-0001-0891-8380
Iraq

Publication Date

October 6, 2026

Submission Date

May 6, 2025

Acceptance Date

October 10, 2025

Published in Issue

Year 2026 Volume: 16 Number: 10

IZ

https://izlik.org/JA22RM98RH

Cite

RIS / Bibtex

APA

Salih, A., & Al-Majidi, A. J. (2026). A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS. TWMS Journal of Applied and Engineering Mathematics, 16(10), 1234-1254. https://izlik.org/JA22RM98RH

AMA

1.Salih A, Al-Majidi AJ. A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS. JAEM. 2026;16(10):1234-1254. https://izlik.org/JA22RM98RH

Chicago

Salih, Ahmed, and Arkan Jebur Al-Majidi. 2026. “A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS”. TWMS Journal of Applied and Engineering Mathematics 16 (10): 1234-54. https://izlik.org/JA22RM98RH.

EndNote

Salih A, Al-Majidi AJ (October 1, 2026) A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS. TWMS Journal of Applied and Engineering Mathematics 16 10 1234–1254.

IEEE

[1]A. Salih and A. J. Al-Majidi, “A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS”, JAEM, vol. 16, no. 10, pp. 1234–1254, Oct. 2026, [Online]. Available: https://izlik.org/JA22RM98RH

ISNAD

Salih, Ahmed - Al-Majidi, Arkan Jebur. “A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS”. TWMS Journal of Applied and Engineering Mathematics 16/10 (October 1, 2026): 1234-1254. https://izlik.org/JA22RM98RH.

JAMA

1.Salih A, Al-Majidi AJ. A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS. JAEM. 2026;16:1234–1254.

MLA

Salih, Ahmed, and Arkan Jebur Al-Majidi. “A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 10, Oct. 2026, pp. 1234-5, https://izlik.org/JA22RM98RH.

Vancouver

1.Ahmed Salih, Arkan Jebur Al-Majidi. A FLEXIBLE UNIT CHEN QUANTILE REGRESSION MODEL FOR BOUNDED RESPONSE DATA: ESTIMATION, MODEL DIAGNOSTICS, AND APPLICATIONS. JAEM [Internet]. 2026 Oct. 1;16(10):1234-5. Available from: https://izlik.org/JA22RM98RH