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

Maher Kachour, Hassan S. Bakouch (), Mustapha Muhammad, Badamasi Abba, Lamia Alyami and Sadiah M. A. Aljeddani ()
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Maher Kachour: Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093, Kuwait
Hassan S. Bakouch: Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
Mustapha Muhammad: Department of Mathematics, Guangdong University of Petrochemical Technology, Maoming 525000, China
Badamasi Abba: School of Mathematics and Statistics, Central South University, Changsha 410083, China
Lamia Alyami: Department of Mathematics, College of Sciences and Arts, Najran University, Najran 11001, Saudi Arabia
Sadiah M. A. Aljeddani: Mathematics Department, Al-Lith University College, Umm Al-Qura University, Al-Lith 21961, Saudi Arabia

Mathematics, 2025, vol. 13, issue 11, 1-20

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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