A Flexible Truncated (u,v)-Half-Normal Distribution: Properties, Estimation and Applications

Kachour, Maher; Bakouch, Hassan S.; Muhammad, Mustapha; Abba, Badamasi; Alyami, Lamia; Aljeddani, Sadiah M. A.

doi:10.3390/math13111740

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A Flexible Truncated (u,v)-Half-Normal Distribution: Properties, Estimation and Applications

by

Maher Kachour

¹,

Hassan S. Bakouch

^2,*

,

Mustapha Muhammad

³,

Badamasi Abba

⁴,

Lamia Alyami

⁵ and

Sadiah M. A. Aljeddani

^6,*

¹

Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093, Kuwait

²

Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia

³

Department of Mathematics, Guangdong University of Petrochemical Technology, Maoming 525000, China

⁴

School of Mathematics and Statistics, Central South University, Changsha 410083, China

⁵

Department of Mathematics, College of Sciences and Arts, Najran University, Najran 11001, Saudi Arabia

⁶

Mathematics Department, Al-Lith University College, Umm Al-Qura University, Al-Lith 21961, Saudi Arabia

^*

Authors to whom correspondence should be addressed.

Mathematics 2025, 13(11), 1740; https://doi.org/10.3390/math13111740 (registering DOI)

Submission received: 29 April 2025 / Revised: 21 May 2025 / Accepted: 22 May 2025 / Published: 24 May 2025

(This article belongs to the Special Issue Methodology and Application in Computational Statistics and Data Science)

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Abstract

This study introduces the truncated

(u, v)

-half-normal distribution, a novel probability model defined on the bounded interval

(u, v)

, with parameters

σ

and b. This distribution is designed to model processes with restricted domains, ensuring realistic and analytically tractable outcomes. Some key properties of the proposed model, including its cumulative distribution function, probability density function, survival function, hazard rate, and moments, are derived and analyzed. Parameter estimation of

σ

and b is achieved through a hybrid approach, combining maximum likelihood estimation (MLE) for

σ

and a likelihood-free-inspired technique for b. A sensitivity analysis highlighting the dependence of

σ

on b, and an optimal estimation algorithm is proposed. The proposed model is applied to two real-world data sets, where it demonstrates superior performance over some existing models based on goodness-of-fit criteria, such as the known AIC, BIC, CAIC, KS, AD, and CvM statistics. The results emphasize the model’s flexibility and robustness for practical applications in modeling data with bounded support.

Keywords: half normal distribution; moments; simulation; parameter estimation; sensitivity analysis; testing algorithm

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MDPI and ACS Style

Kachour, M.; Bakouch, H.S.; Muhammad, M.; Abba, B.; Alyami, L.; Aljeddani, S.M.A. A Flexible Truncated (u,v)-Half-Normal Distribution: Properties, Estimation and Applications. Mathematics 2025, 13, 1740. https://doi.org/10.3390/math13111740

AMA Style

Kachour M, Bakouch HS, Muhammad M, Abba B, Alyami L, Aljeddani SMA. A Flexible Truncated (u,v)-Half-Normal Distribution: Properties, Estimation and Applications. Mathematics. 2025; 13(11):1740. https://doi.org/10.3390/math13111740

Chicago/Turabian Style

Kachour, Maher, Hassan S. Bakouch, Mustapha Muhammad, Badamasi Abba, Lamia Alyami, and Sadiah M. A. Aljeddani. 2025. "A Flexible Truncated (u,v)-Half-Normal Distribution: Properties, Estimation and Applications" Mathematics 13, no. 11: 1740. https://doi.org/10.3390/math13111740

APA Style

Kachour, M., Bakouch, H. S., Muhammad, M., Abba, B., Alyami, L., & Aljeddani, S. M. A. (2025). A Flexible Truncated (u,v)-Half-Normal Distribution: Properties, Estimation and Applications. Mathematics, 13(11), 1740. https://doi.org/10.3390/math13111740

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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A Flexible Truncated (u,v)-Half-Normal Distribution: Properties, Estimation and Applications

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