A novel one-parameter tri-modal alpha-skew logistic distribution: mathematical and reliability theory with applications to distant astronomical galaxies and biomedical data

Reda Elbarougy; Jondeep Das; Partha Jyoti Hazarika; G. G. Hamedani; Anupama Nandi; Mohamed S. Eliwa; Reda Elbarougy; Jondeep Das; Partha Jyoti Hazarika; G. G. Hamedani; Anupama Nandi; Mohamed S. Eliwa

doi:10.3934/math.2026305

AIMS Mathematics

2026, Volume 11, Issue 3: 7436-7467. doi: 10.3934/math.2026305

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A novel one-parameter tri-modal alpha-skew logistic distribution: mathematical and reliability theory with applications to distant astronomical galaxies and biomedical data

1.
Department of Artificial Intelligence and Data Science, College of Computer Science and Engineering, University of Ha'il, Saudi Arabia
2.
Department of Statistics, Bhattadev University, Bajali, Assam, India
3.
Department of Statistics, Dibrugarh University, Dibrugarh, Assam, India
4.
Department of Mathematical and Statistical Sciences, Marquette University, USA
5.
Department of Statistics and Operations Research, College of Science, Qassim University, Saudi Arabia

Received: 07 January 2026 Revised: 27 February 2026 Accepted: 16 March 2026 Published: 20 March 2026
MSC : 60E05, 62E15, 62F10, 62N05, 62P99

In this paper, we presented a novel family of heavy-tailed continuous probability distributions tailored to model data exhibiting trimodal features with various kurtosis levels in asymmetric, under-dispersed datasets across various categories of risk. The proposed model enhanced the alpha-skew logistic distribution, providing significant adaptability to represent asymmetry and various tail characteristics. Key statistical properties were established, and additional characterizations were offered. Mathematical and numerical analyses indicated that the model efficiently handled asymmetric data, especially under conditions of under-dispersion. The associated hazard rate function displayed various forms, demonstrating the model's versatility in reliability and survival analysis. Parameter estimation was conducted using the maximum likelihood method, and simulation studies were employed to assess the performance of estimators in small samples. The practical applicability of the model was further demonstrated through analyses of two real datasets. Finally, comparative analyses with alternative models employing a likelihood ratio test substantiated its better performance.
- statistical model,
- multi-modality property,
- failure analysis,
- truncated moments,
- simulation,
- likelihood ratio test,
- data analysis
Citation: Reda Elbarougy, Jondeep Das, Partha Jyoti Hazarika, G. G. Hamedani, Anupama Nandi, Mohamed S. Eliwa. A novel one-parameter tri-modal alpha-skew logistic distribution: mathematical and reliability theory with applications to distant astronomical galaxies and biomedical data[J]. AIMS Mathematics, 2026, 11(3): 7436-7467. doi: 10.3934/math.2026305

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Abstract

In this paper, we presented a novel family of heavy-tailed continuous probability distributions tailored to model data exhibiting trimodal features with various kurtosis levels in asymmetric, under-dispersed datasets across various categories of risk. The proposed model enhanced the alpha-skew logistic distribution, providing significant adaptability to represent asymmetry and various tail characteristics. Key statistical properties were established, and additional characterizations were offered. Mathematical and numerical analyses indicated that the model efficiently handled asymmetric data, especially under conditions of under-dispersion. The associated hazard rate function displayed various forms, demonstrating the model's versatility in reliability and survival analysis. Parameter estimation was conducted using the maximum likelihood method, and simulation studies were employed to assess the performance of estimators in small samples. The practical applicability of the model was further demonstrated through analyses of two real datasets. Finally, comparative analyses with alternative models employing a likelihood ratio test substantiated its better performance.

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