A new Beta distribution with interdisciplinary data analysis

Uthumporn Panitanarak; Aliyu Ismail Ishaq; Ahmad Abubakar Suleiman; Hanita Daud; Narinderjit Singh Sawaran Singh; Abdullahi Ubale Usman; Najwan Alsadat; Mohammed Elgarhy; Uthumporn Panitanarak; Aliyu Ismail Ishaq; Ahmad Abubakar Suleiman; Hanita Daud; Narinderjit Singh Sawaran Singh; Abdullahi Ubale Usman; Najwan Alsadat; Mohammed Elgarhy

doi:10.3934/math.2025391

AIMS Mathematics

2025, Volume 10, Issue 4: 8495-8527. doi: 10.3934/math.2025391

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Research article Special Issues

A new Beta distribution with interdisciplinary data analysis

1.
Department of Biostatistics, Faculty of Public Health, Mahidol University, Thailand
2.
Department of Statistics, Ahmadu Bello University, Zaria, Nigeria
3.
Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Seri Iskandar, Malaysia
4.
Faculty of Data Science and Information Technology, INTI International University, Persiaran Perdana BBN Putra Nilai, Malaysia
5.
School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China
6.
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
7.
Department of Basic Sciences, Higher Institute of Administrative Sciences, Belbeis, AlSharkia, Egypt

Received: 22 August 2024 Revised: 08 March 2025 Accepted: 13 March 2025 Published: 14 April 2025
MSC : 60E05, 62F10, 62H12

Several families of Beta distributions, such as Beta of the first kind, Beta of the second kind, and Beta of the third kind, have been proposed in the literature for modeling random phenomena. This study introduced a new member of the Beta family called the New Beta (NE-Beta) distribution using a logarithmic transformation approach. This new model is highly flexible and capable of analyzing both positive and negative data, making it suitable for a wide range of interdisciplinary applications. The NE-Beta distribution exhibits nearly symmetric, right-skewed, or left-skewed density functions and featured an increasing or decreasing hazard functions, which are crucial for accurately modeling practical scenarios across various fields. Some properties of the new distribution were derived, and the parameter estimation was obtained by utilizing various approaches. To demonstrate the efficacy of the NE-Beta distribution, it was applied to multiple datasets, including exchange rate returns (finance), biomedical data, engineering reliability data, and hydrological data. The results indicate that the proposed NE-Beta model outperforms its competitors across these diverse domains.
- Beta distribution,
- finance,
- logarithmic transformation,
- skewness,
- Rényi entropy,
- economic resources
Citation: Uthumporn Panitanarak, Aliyu Ismail Ishaq, Ahmad Abubakar Suleiman, Hanita Daud, Narinderjit Singh Sawaran Singh, Abdullahi Ubale Usman, Najwan Alsadat, Mohammed Elgarhy. A new Beta distribution with interdisciplinary data analysis[J]. AIMS Mathematics, 2025, 10(4): 8495-8527. doi: 10.3934/math.2025391

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Abstract

Several families of Beta distributions, such as Beta of the first kind, Beta of the second kind, and Beta of the third kind, have been proposed in the literature for modeling random phenomena. This study introduced a new member of the Beta family called the New Beta (NE-Beta) distribution using a logarithmic transformation approach. This new model is highly flexible and capable of analyzing both positive and negative data, making it suitable for a wide range of interdisciplinary applications. The NE-Beta distribution exhibits nearly symmetric, right-skewed, or left-skewed density functions and featured an increasing or decreasing hazard functions, which are crucial for accurately modeling practical scenarios across various fields. Some properties of the new distribution were derived, and the parameter estimation was obtained by utilizing various approaches. To demonstrate the efficacy of the NE-Beta distribution, it was applied to multiple datasets, including exchange rate returns (finance), biomedical data, engineering reliability data, and hydrological data. The results indicate that the proposed NE-Beta model outperforms its competitors across these diverse domains.

References

[1]	M. K. Simon, Probability distributions involving Gaussian random variables: A handbook for engineers and scientists, New York: Springer, 2002. https://doi.org/10.1007/978-0-387-47694-0
[2]	A. N. O'Connor, Probability distributions used in reliability engineering, Reliability information analysis center, 2011.
[3]	A. I. Ishaq, U. Panitanarak, A. A. Abiodun, A. A. Suleiman, H. Daud, The generalized Odd Maxwell-Kumaraswamy distribution: Its properties and applications, Contemp. Math., 5 (2024), 711–742. https://doi.org/10.37256/cm.5120242888 doi: 10.37256/cm.5120242888
[4]	J. B. McDonald, Y. J. Xu, A generalization of the Beta distribution with applications, J. Econometrics, 66 (1995), 133–152. https://doi.org/10.1016/0304-4076(94)01612-4 doi: 10.1016/0304-4076(94)01612-4
[5]	M. Y. Sulaiman, W. M. Hlaing Oo, M. Abd Wahab, A. Zakaria, Application of Beta distribution model to Malaysian sunshine data, Renew. Energy, 18 (1999), 573–579. https://doi.org/10.1016/S0960-1481(99)00002-6 doi: 10.1016/S0960-1481(99)00002-6
[6]	M. Graf, D. Nedyalkova, Modeling of income and indicators of poverty and social exclusion using the generalized Beta distribution of the second kind, Rev. Income Wewlth, 60 (2014), 821–842. https://doi.org/10.1111/roiw.12031 doi: 10.1111/roiw.12031
[7]	M. Raschke, Empirical behaviour of tests for the Beta distribution and their application in environmental research, Stoch. Environ. Res. Risk Assess., 25 (2011), 79–89. https://doi.org/10.1007/s00477-010-0410-3 doi: 10.1007/s00477-010-0410-3
[8]	B. Kim, K. F. Reinschmidt, Probabilistic forecasting of project duration using Bayesian inference and the Beta distribution, J. Constr. Eng. M., 135 (2009), 178–186. https://doi.org/10.1061/(ASCE)0733-9364(2009)135:3(178) doi: 10.1061/(ASCE)0733-9364(2009)135:3(178)
[9]	P. Chen, X. Xiao, Novel closed-form point estimators for the Beta distribution, Stat. Theory Relat. F., 9 (2025), 12–33. http://doi.org/10.1080/24754269.2024.2419360 doi: 10.1080/24754269.2024.2419360
[10]	A. A. Suleiman, H. Daud, N. S. S. Singh, M. Othman, A. I. Ishaq, R. Sokkalingam, A novel Odd Beta prime-logistic distribution: Desirable mathematical properties and applications to engineering and environmental data, Sustainability, 15 (2023), 10239. https://doi.org/10.3390/su151310239 doi: 10.3390/su151310239
[11]	L. Chen, V. Singh, Generalized Beta distribution of the second kind for flood frequency analysis, Entropy, 19 (2017), 254. https://doi.org/10.3390/e19060254 doi: 10.3390/e19060254
[12]	A. A. Suleiman, H. Daud, N. S. S. Singh, A. I. Ishaq, M. Othman, A new Odd Beta prime-burr X distribution with applications to petroleum rock sample data and COVID-19 mortality rate, Data, 8 (2023), 143. https://doi.org/10.3390/data8090143 doi: 10.3390/data8090143
[13]	J. B. McDonald, Model selection: some generalized distributions, Commun. Stat. Theor. M., 16 (1987), 1049–1074. https://doi.org/10.1080/03610928708829422 doi: 10.1080/03610928708829422
[14]	A. A. Suleiman, H. Daud, A. I. Ishaq, M. Othman, R. Sokkalingam, A. Usman, et al., The Odd Beta prime inverted Kumaraswamy distribution with application to COVID-19 mortality rate in Italy, Eng. proc., 56 (2023), 218. https://doi.org/10.3390/ASEC2023-16310 doi: 10.3390/ASEC2023-16310
[15]	A. A. Suleiman, H. Daud, M. Othman, N. S. S. Singh, A. I. Ishaq, R. Sokkalingam, et al., A novel extension of the Fréchet distribution: statistical properties and application to groundwater pollutant concentrations, J. Data Sci. Insight., 1 (2023), 8–24.
[16]	A. K. Gupta, D. K. Nagar, Matrix‐variate Beta distribution, Int. J. Math. Math. Sci., 24 (2000), 449–459. https://doi.org/10.1155/S0161171200002398 doi: 10.1155/S0161171200002398
[17]	L. Cardeno, D. K. Nagar, L. E. Sánchez, Beta type 3 distribution and its multivariate, Tamsui Oxford J. Math. Sci., 21 (2005), 225–241.
[18]	A. I. Ishaq, A. A. Suleiman, H. Daud, N. S. S. Singh, M. Othman, R. Sokkaalingam, et al., Log-Kumaraswamy distribution: its features and applications, Front. Appl. Math. Stat., 9 (2023), 1258961. https://doi.org/10.3389/fams.2023.1258961 doi: 10.3389/fams.2023.1258961
[19]	A. I. Ishaq, A. A. Suleiman, A. Usman, H. Daud, R. Sokkalingam, Transformed log-burr Ⅲ distribution: Structural features and application to milk production, Eng. proc., 56 (2023), 322. https://doi.org/10.3390/ASEC2023-15289 doi: 10.3390/ASEC2023-15289
[20]	A. Usman, A. I. Ishaq, A. A. Suleiman, M. Othman, H. Daud, Y. Aliyu, Univariate and bivariate log-topp-leone distribution using censored and uncensored datasets, Comput. Sci. Math. Forum, 7 (2023), 32. https://doi.org/10.3390/IOCMA2023-14421 doi: 10.3390/IOCMA2023-14421
[21]	A. A. Suleiman, H. Daud, A. A. Ishaq, M. Kayid, R. Sokkalingam, Y. Hamed, et al., A new Weibull distribution for modeling complex biomedical data, J. Radiat. Res. Appl. Sci., 17 (2024), 101190. https://doi.org/10.1016/j.jrras.2024.101190 doi: 10.1016/j.jrras.2024.101190
[22]	H. Daud, A. A. Suleiman, A. I. Ishaq, N. Alsadat, M. Elgarhy, A. Usman, et al., A new extension of the Gumbel distribution with biomedical data analysis, J. Radiat. Res. Appl. Sci., 17 (2024), 101055. https://doi.org/10.1016/j.jrras.2024.101055 doi: 10.1016/j.jrras.2024.101055
[23]	A. M. Almarashi, M. Elgarhy, A new muth generated family of distributions with applications, J. Nonlinear Sci. Appl., 11 (2018), 1171–1184.
[24]	M. A. ul Haq, M. Elgarhy, The Odd Frechet-G family of probability distributions, J. Stat. Appl. Probab., 7 (2018), 185–201. https://doi.org/10.18576/jsap/070117 doi: 10.18576/jsap/070117
[25]	S. Alkarni, A. Z. Afify, I. Elbatal, M. Elgarhy, The extended inverse Weibull distribution: properties and applications, Complexity, 2020 (2020), 3297693. https://doi.org/10.1155/2020/3297693 doi: 10.1155/2020/3297693
[26]	M. Elgarhy, M. Shakil, G. Kibria, Exponentiated Weibull-exponential distribution with applications, Appl. Appl. Math., 12 (2017), 5.
[27]	S. A. Alyami, I. Elbatal, N. Alotaibi, E. M. Almetwally, H. M. Okasha, M. Elgarhy, Topp–Leone modified Weibull model: Theory and applications to medical and engineering data, Appl. Sci., 12 (2022), 10431. https://doi.org/10.3390/app122010431 doi: 10.3390/app122010431
[28]	M. M. Salama, E. S. A. El-Sherpieny, A. E. A. Abd-elaziz, The length-biased weighted exponentiated inverted exponential distribution: properties and estimation, Comput. J. Math. Stat. Sci., 2 (2023), 181–196. https://doi.org/10.21608/cjmss.2023.215674.1009 doi: 10.21608/cjmss.2023.215674.1009
[29]	M. Shakil, T. Hussain, Z. U. Rehman, A. Khadim, M. Sirajo, J. N. Singh, et al., A Skew product distribution with applications, Comput. J. Math. Stat.l Sci., 3 (2024), 432–453. https://doi.org/10.21608/cjmss.2024.283619.1049 doi: 10.21608/cjmss.2024.283619.1049
[30]	M. N. Atchade, A. A. Agbahide, T. Otodji, M. J. Bogninou, A. M. Djibril, A new shifted Lomax-X family of distributions: Properties and applications to actuarial and financial data, Comput. J. Math. Stat. Sci., 4 (2025), 41–71. http://doi.org/10.21608/cjmss.2024.307114.1066 doi: 10.21608/cjmss.2024.307114.1066
[31]	J. N. Kapur, H. C. Saxena, Mathematical statistics: S Chand & Co, New Delhi, 1997.
[32]	H. S. Klakattawi, Survival analysis of cancer patients using a new extended Weibull distribution, PLoS One, 17 (2022), e0264229. https://doi.org/10.1371/journal.pone.0264229 doi: 10.1371/journal.pone.0264229
[33]	A. G. Abubakari, C. C. Kandza-Tadi, E. Moyo, Modified beta inverse flexible Weibull extension distribution, Ann. Data. Sci., 10 (2023), 589–617. https://doi.org/10.1007/s40745-021-00330-3 doi: 10.1007/s40745-021-00330-3
[34]	H. M. Alshanbari, O. H. Odhah, H. Al-Mofleh, Z. Ahmad, S. K. Khosa, A. H. El-Bagoury, A new flexible Weibull extension model: Different estimation methods and modeling an extreme value data, Heliyon, 9 (2023), e21704. https://doi.org/10.1016/j.heliyon.2023.e21704 doi: 10.1016/j.heliyon.2023.e21704
[35]	A. Xu, G. Fang, L. Zhuang, C. Gu, A multivariate student-t process model for dependent tail-weighted degradation data, IISE Trans., 2024 (2024), 1–17. http://doi.org/10.1080/24725854.2024.2389538 doi: 10.1080/24725854.2024.2389538

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