A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data

Alanazi Talal Abdulrahman; Khudhayr A. Rashedi; Tariq S. Alshammari; Eslam Hussam; Amirah Saeed Alharthi; Ramlah H Albayyat; Alanazi Talal Abdulrahman; Khudhayr A. Rashedi; Tariq S. Alshammari; Eslam Hussam; Amirah Saeed Alharthi; Ramlah H Albayyat

doi:10.3934/math.2025172

AIMS Mathematics

2025, Volume 10, Issue 2: 3710-3733. doi: 10.3934/math.2025172

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Research article

A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data

1.
Department of Mathematics, College of Science University of Ha'il, Hail, Saudi Arabia
2.
Department of Accounting, College of Business Administration in Hawtat Bani Tamim, Prince Sattam bin Abdulaziz University, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, P.O. Box 11099, Taif University, Taif 21944, Saudi Arabia
4.
Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia

Received: 09 December 2024 Revised: 07 February 2025 Accepted: 12 February 2025 Published: 25 February 2025
MSC : 60B12, 62G30

In statistical modeling, generating a novel family of distributions is essential to develop new and adaptable models to analyze various data sets. This paper presents a new asymmetric extension of the Rayleigh distribution called the generalized Kumaraswamy Rayleigh model. The proposed distribution can fit symmetric, complex, heavy-tailed, and asymmetric data sets. Several key mathematical and statistical results were investigated, including moments, moment-generating functions, variance, dispersion index, skewness, and kurtosis for the suggested model. In addition, various estimation strategies, including maximum likelihood estimation and Bayes estimation, were used to estimate the model parameters. The Metropolis-Hastings technique was used for Bayesian estimates under the square error loss function. A comprehensive simulation study was used to evaluate the performance of the derived estimators. The model's flexibility was tested on two data sets from the industrial domain, revealing that it offers greater flexibility compared to existing distributions.
- Bayesian estimator,
- heavy-tailed,
- industrial domain,
- Metropolis-Hastings technique,
- simulation experiments,
- square error loss function
Citation: Alanazi Talal Abdulrahman, Khudhayr A. Rashedi, Tariq S. Alshammari, Eslam Hussam, Amirah Saeed Alharthi, Ramlah H Albayyat. A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data[J]. AIMS Mathematics, 2025, 10(2): 3710-3733. doi: 10.3934/math.2025172

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Abstract

In statistical modeling, generating a novel family of distributions is essential to develop new and adaptable models to analyze various data sets. This paper presents a new asymmetric extension of the Rayleigh distribution called the generalized Kumaraswamy Rayleigh model. The proposed distribution can fit symmetric, complex, heavy-tailed, and asymmetric data sets. Several key mathematical and statistical results were investigated, including moments, moment-generating functions, variance, dispersion index, skewness, and kurtosis for the suggested model. In addition, various estimation strategies, including maximum likelihood estimation and Bayes estimation, were used to estimate the model parameters. The Metropolis-Hastings technique was used for Bayesian estimates under the square error loss function. A comprehensive simulation study was used to evaluate the performance of the derived estimators. The model's flexibility was tested on two data sets from the industrial domain, revealing that it offers greater flexibility compared to existing distributions.

References

[1]	V. Verevka, E. Epichenko, Developing a model for predicting bankruptcy of construction industry enterprises, Econom. Anal. Theory Pract., 23 (2024), 878–892. https://doi.org/10.24891/ea.23.5.878 doi: 10.24891/ea.23.5.878
[2]	V. V. Barskov, Y. A. Dubolazova, A. A. Maykova, E. A. Konnikov, Modeling the probability of companies bankruptcy in the construction industry, Soft Meas. Comput., 2 (2023), 5–15. https://doi.org/10.36871/2618-9976.2024.02.001 doi: 10.36871/2618-9976.2024.02.001
[3]	A. Alzaatreh, C. Lee, F. Famoye, A new method for generating families of continuous distributions, METRON, 71 (2013), 63–79. https://doi.org/10.1007/s40300-013-0007-y doi: 10.1007/s40300-013-0007-y
[4]	T. G. Ieren, S. S. Abdulkadir, A. A. Issa, Odd Lindley- Rayleigh distribution its properties and applications to simulated and real life datasets, J. Adv. Math. Comput. Sci., 35 (2020), 68–88. https://doi.org/10.9734/jamcs/2020/v35i130240 doi: 10.9734/jamcs/2020/v35i130240
[5]	F. H. Riad, B. Alruwaili, E. M. Almetwally, E. Hussam, Fuzzy reliability analysis of the COVID‐19 mortality rate using a new modified Kies Kumaraswamy model, J. Math., 2022 (2022), 3427521. https://doi.org/10.1155/2022/3427521 doi: 10.1155/2022/3427521
[6]	A. EL-Helbawy, M. Hegazy, A. Abd EL-Hady, Statistical properties and applications of the discrete exponentiated modified Topp-Leone Chen distribution, J. Bus. Environ. Sci., 4 (2025), 106–132.
[7]	E. Altun, D. Bhati, N. M. Khan, A new approach to model the counts of earthquakes: INARPQX(1) process, SN Appl. Sci., 3 (2021), 274. https://doi.org/10.1007/s42452-020-04109-8 doi: 10.1007/s42452-020-04109-8
[8]	R. Alotaibi, E. M. Almetwally, H. Rezk, Reliability analysis of Kavya Manoharan Kumaraswamy distribution under generalized progressive hybrid data, Symmetry, 15 (2023), 1671. https://doi.org/10.3390/sym15091671 doi: 10.3390/sym15091671
[9]	R. Maya, M. R. Irshad, C. Chesneau, S. L. Nitin, D. S. Shibu, On discrete Poisson–Mirra distribution: Regression, INAR (1) process and applications, Axioms, 11 (2022), 193. https://doi.org/10.3390/axioms11050193 doi: 10.3390/axioms11050193
[10]	M. A. Meraou, M. Z. Raqab, F. B. Almathkour, Analyzing insurance data with an alpha power transformed exponential Poisson model, Ann. Data Sci., 2024. https://doi.org/10.1007/s40745-024-00554-z
[11]	M. A. Meraou, N. M. Al-Kandari, M. Z. Raqab, D. Kundu, Analysis of skewed data by using compound Poisson exponential distribution with applications to insurance claims, J. Stat. Comput. Simul., 92 (2021), 928–956. https://doi.org/10.1080/00949655.2021.1981324 doi: 10.1080/00949655.2021.1981324
[12]	M. A. Meraou, N. Al-Kandari, M. Z. Raqab, Univariate and bivariate compound models based on random sum of variates with application to the insurance losses data, J. Stat. Theory Pract., 16 (2022), 56. https://doi.org/10.1007/s42519-022-00282-8 doi: 10.1007/s42519-022-00282-8
[13]	M. A. Meraou, M. Z. Raqab, D. Kundu, F. A. Alqallaf, Inference for compound truncated Poisson log-normal model with application to maximum precipitation data, Comm. Statist. Simulation Comput., 2024. https://doi.org/10.1080/03610918.2024.2328168
[14]	H. Alrweili, E. S. Alotaibi, Bayesian and non-bayesian estimation of Marshall-Olkin XLindley distribution in presence of censoring, cure fraction, and application on medical data, Alexandria Eng. J., 112 (2025), 633–646. https://doi.org/10.1016/j.aej.2024.10.108 doi: 10.1016/j.aej.2024.10.108
[15]	H. Alrweili, Analysis of recent decade rainfall data with new exponential-exponential distribution: Inference and applications, Alexandria Eng. J., 95 (2024), 306–320. https://doi.org/10.1016/j.aej.2024.03.075 doi: 10.1016/j.aej.2024.03.075
[16]	H. Alrweili, On the analysis of environmental and engineering data using alpha power transformed cosine moment exponential model, Int. J. Anal. Appl., 22 (2024), 99. https://doi.org/10.28924/2291-8639-22-2024-99 doi: 10.28924/2291-8639-22-2024-99
[17]	Z. M. Nofal, E. Altun, A. Z. Afify, M. Ahsanullah, The generalized kumaraswamy-G family of distributions, J. Stat. Theory Appl., 18 (2019), 329–342. https://doi.org/10.2991/jsta.d.191030.001 doi: 10.2991/jsta.d.191030.001
[18]	C. D. Obi, P. O. Chukwuma, P. Chinyere, C. P. Igbokwe, P. O. Ibeakuzie, I. C. Anabike, A novel extension of Rayleigh distribution: Characterization, estimation, simulations and applications, J. Xidian Univ., 18 (2024), 177–188. https://doi.org/10.5281/Zenodo.12664617 doi: 10.5281/Zenodo.12664617
[19]	M. Jallal, A. Ahmad, R. Tripathi, Weibull-Power Rayleigh distribution with applications related to distinct fields of science, Realibilty Theory Appl., 2 (2022), 272–290.
[20]	A. Aijaz, S. Q. ul-Ain, A. Afaq, T. Rajnee, Inverse Weibull-Rayleigh distribution characterisation with applications related to cancer data, Reliab. Theory Appl., 16 (2021), 364–382.
[21]	H. Abdulsalam, Y. Abubakar, G. DikkoH, On the properties and applications of a new extension of exponentiated Rayleigh distribution, FUDMA J. Sci., 5 (2021), 377–398. https://doi.org/10.33003/fjs-2021-0502-459 doi: 10.33003/fjs-2021-0502-459
[22]	M. Javed, S. M. Asim, A. Khalil, S. F. Shah, A. Zahra, New Rayleigh flexible Weibull extension (RFWE) distribution with applications to real and simulated data, Model. Simul. Eng., 2022 (2022), 7718284. https://doi.org/10.1155/2022/7718284 doi: 10.1155/2022/7718284
[23]	B. C. Arnold, N. Balskrishnan, H. N. Nagaraja, A first course in order statistics, In: Classics in applied mathematics, Society for Industrial and Applied Mathematics, 2008.
[24]	H. A. David, H. N. Nagaraja, Order statistics, John Wiley & Sons, Inc., 2004.
[25]	M. N. Atchadé, 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://dx.doi.org/10.21608/cjmss.2024.307114.1066 doi: 10.21608/cjmss.2024.307114.1066
[26]	M. Kamal, R. Aldallal, S. G. Nassr, A. Al Mutairi, M. Yusuf, M. S. Mustafa, et al., A new improved form of the Lomax model: Its bivariate extension and an application in the financial sector, Alexandria Eng. J., 75 (2023), 127–138. https://doi.org/10.1016/j.aej.2023.05.027 doi: 10.1016/j.aej.2023.05.027
[27]	H. Yu, Z. Shang, Z. Wang, Analysis of the current situation of the construction industry in Saudi Arabia and the factors affecting It: An empirical study, Sustainability, 16 (2024), 6756. https://doi.org/10.3390/su16166756 doi: 10.3390/su16166756

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