New Distribution with Statistical Properties and Classical Estimation Method
DOI:
https://doi.org/10.30526/39.4.4445Keywords:
: Shanker distribution, Rayleigh distribution, survival function, moment generating function, quantile functionAbstract
In the present study, we propose a new model, identified as the Shanker Rayleigh distribution, which is derived by combining the survival functions of the classical Rayleigh and Shanker distributions, both of which have a scale parameter only. We developed this hybrid model to offer the additional modeling flexibility required for complex lifespans that single-unit distributions cannot accurately represent. Theoretical characteristics of the distribution (probability density function, cumulative distribution function, survival, and hazard rate function) are derived in closed form. In addition, important distributional properties, namely the raw and central moments, moment-generating function, and quantile function, are methodically examined and developed from two statistical methods, maximum likelihood estimation (MLE) and ordinary least squares (OLS), for estimating the parameter of the proposed model, and their efficiency was assessed by applying them to real data to demonstrate the new models’ ability to better apply the data. In addition, this proposal was applied for scientific purposes through the analysis of real data
References
1. Murthy DNP, Xie M, Jiang R. weibull models. Hoboken (NJ): John Wiley & Sons; 2004.
2. Kumar S, Jain M. Shifted mixture model using weibull, lognormal, and gamma distributions. Natl Acad Sci. Lett. 2023;46(6):539–545. https://doi.org/10.1007/s40009-023-01287-y
3. Newcomb S. A generalized theory of the combination of observations so as to obtain the best result. Am J Math. 1886;8(4):343–366. https://doi.org/10.2307/2369375
4. Khongthip P, Patummasut M, Bodhisuwan W. The discrete weighted exponential distribution and its applications. Songklanakarin J Sci Technol. 2018;40(5).1105-1114. https://doi.org/10.14456/sjst-psu.2018.137.
5. Huang H. Three methods for combining probability distributions and an alternative to random-effects meta-analysis. Metrology. 2025;6(1). 1 https://doi.org/10.3390/metrology6010001
6. Bishop CM, Nasrabadi NM. Pattern recognition and machine learning. New York: Springer; 2006.
7. Shanker R. Shanker distribution and its applications. Int J Stat Appl. 2015;5(6):338–348.
8. Al-Zahrani B, Al-Omari AI. Exponentiated Lindley distribution with applications to lifetime data. J Appl Math Comput Mech. 2015;14(4):5–15. https://doi.org/10.17512/jamcm.2015.4.01
9. Bagui S, Liu J, Zhang S. Deriving mixture distributions through moment-generating functions. J Stat Theory Appl. 2020;19(3):383–390. https://doi.org/10.2991/jsta.d.200826.001
10. Mohsin LA, Kalt HG. Alpha logarithm-Rayleigh distribution with application. In: Proceedings of the 8th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT); 2024. p. 1–6.
11. Mahmoud MR, Amer NM. New mixture of two beta exponential distributions and income distribution. J Stat Appl Probab. 2022, 11(2):395–402. http://doi.org/10.18576/jsap/110203
12. Jin Y, Yin Z, Zhu W, Lee D. Improving spatiotemporal data fusion method in multiband images by distributing variates. Sci Rep. 2025;15(1):20854. https://doi.org/10.1038/s41598-025-05016-x
13. Khamees AK, Abdelaziz AY, Ali ZM, Alharthi MM, Ghoneim SSM, Eskaros MR, Attia M. Mixture probability distribution functions using novel metaheuristic method in wind speed modeling. Ain Shams Eng J. 2022;13(3):101613. https://doi.org/10.1016/j.asej.2021.10.008
14. Raftery AE, Gneiting T, Balabdaoui F, Polakowski M. Using Bayesian model averaging to calibrate forecast ensembles. Mon Weather Rev. 2005;133(5):1155–1174. https://doi.org/10.1175/MWR2906.1
15. Melnykov I, Steczek S. Modeling time-dependent population proportions in a finite mixture model setting. Adv Data Anal Classif. 2025. Advance online publication. https://doi.org/10.1007/s11634-025-00643-8
16. Naderi M, Mozafari M, Okhli K. Finite mixture modeling via skew-laplace birnbaum-saunders distribution. Stat Theory Appl. 2020;19(1):49–58. https://doi.org/10.2991/jsta.d.200224.008
17. Nie K, Sinha BK, Hedayat AS. Unbiased estimation of reliability function from a mixture of two exponential distributions based on a single observation. Stat Probab Lett. 2017;127:7–13. https://doi.org/10.1016/j.spl.2017.03.026
18. Ahmed NR. Decentralized Gaussian mixture fusion through unified quotient approximations. arXiv. 2019;arXiv:1907.04008. https://doi.org/10.48550/arXiv.1907.04008
19. Kumar J, Nain A. Exploring new mixtures of distribution to model skewed and heavy tailed data. Stat Transit New Ser. 2025;26(4):55–68. https://doi.org/10.59139/stattrans-2025-039
20. Falhi FH, Hmood MY. Estimation of copula density using the wavelet transform. Baghdad Sci J. 2024;21(11):18. https://doi.org/10.21123/bsj.2024.9673
21. Anjana V. Estimation of the scale parameter of triangular distribution using absolved order statistics. J Kerala Stat Assoc. 2021;32(1):51–74.
22. Shanker R, Shukla KK. Power Shanker distribution and its application. Turkiye Klin J Biostat. 2017;9(3):175–187. https://doi.org/10.5336/bioistat.2016-53178
23. Maleki Jebely F, Zare K, Deiri E. Efficient estimation of the PDF and the CDF of the inverse Rayleigh distribution. J Stat Comput Simul. 2018;88(1):75–88. https://doi.org/10.1080/00949655.2017.1378656
24. Miura K. An introduction to maximum likelihood estimation and information geometry. Interdiscip Inf Sci. 2011;17(3):155–174. https://doi.org/10.4036/iis.2011.155
25. De Souza SVC, Junqueira RG. A procedure to assess linearity by ordinary least squares method. Anal Chim Acta. 2005;552(1–2):25–35. https://doi.org/10.1016/j.aca.2005.07.043
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Ibn AL-Haitham Journal For Pure and Applied Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.
licenseTermsHow to Cite
