An innovative discrete distribution for modeling genotoxicity data: Applications in pharmacology and environmental health

Amal S. Hassan; Eslam Abdelhakim Seyam; Asma Ahmad Alzahrani; Omar A. Saudi; Amal S. Hassan; Eslam Abdelhakim Seyam; Asma Ahmad Alzahrani; Omar A. Saudi

doi:10.3934/math.2026049

AIMS Mathematics

2026, Volume 11, Issue 1: 1145-1174. doi: 10.3934/math.2026049

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An innovative discrete distribution for modeling genotoxicity data: Applications in pharmacology and environmental health

1.
Faculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza, 12613, Egypt
2.
Department of Insurance and Risk Management, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha 65779, Saudi Arabia
4.
Department of Basic Sciences, Higher Institute of Management Sciences (HIMS), El Katameya, New Cairo 3, 11936, Egypt

Received: 18 September 2025 Revised: 19 November 2025 Accepted: 28 November 2025 Published: 15 January 2026
MSC : 60E05, 62E10, 62F10, 62N05, 62P10

This paper proposes a flexible probability mass function for modeling count data, particularly over-dispersed and asymmetric observations. A novel two-parameter discrete distribution, the discrete power inverted Topp–Leone distribution, is presented using a survival discretization technique. The following statistical characteristics are examined: factorial moments, probability-generating function, quantiles, mean, variance, mean residual life, and entropy measures. The best estimators of the unknown parameters were obtained using various techniques, such as maximum likelihood, moments, least squares, Anderson–Darling, and Cramér-von Mises. A simulation study showed that the accuracy of the estimates improves with larger samples, although higher parameter values may affect precision. The findings indicate that the efficiency of these estimation methods varies under different conditions. Applications to liver lesions, chromatid aberrations, and criminal sociology datasets confirm the model's usefulness for discrete count data in fields such as social sciences, pharmacology, and environmental health. Finally, for modeling count data, the new probabilistic model can be employed as a competitive alternative to other existing distributions.
- count distribution,
- discretization,
- survival function,
- Anderson-Darling,
- factorial moments
Citation: Amal S. Hassan, Eslam Abdelhakim Seyam, Asma Ahmad Alzahrani, Omar A. Saudi. An innovative discrete distribution for modeling genotoxicity data: Applications in pharmacology and environmental health[J]. AIMS Mathematics, 2026, 11(1): 1145-1174. doi: 10.3934/math.2026049

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Abstract

This paper proposes a flexible probability mass function for modeling count data, particularly over-dispersed and asymmetric observations. A novel two-parameter discrete distribution, the discrete power inverted Topp–Leone distribution, is presented using a survival discretization technique. The following statistical characteristics are examined: factorial moments, probability-generating function, quantiles, mean, variance, mean residual life, and entropy measures. The best estimators of the unknown parameters were obtained using various techniques, such as maximum likelihood, moments, least squares, Anderson–Darling, and Cramér-von Mises. A simulation study showed that the accuracy of the estimates improves with larger samples, although higher parameter values may affect precision. The findings indicate that the efficiency of these estimation methods varies under different conditions. Applications to liver lesions, chromatid aberrations, and criminal sociology datasets confirm the model's usefulness for discrete count data in fields such as social sciences, pharmacology, and environmental health. Finally, for modeling count data, the new probabilistic model can be employed as a competitive alternative to other existing distributions.

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