Statistical Framework for Modeling Asymmetrical Data with Dual Peaks

K M Sakthivel; G Vidhya  lowast

doi:10.17485/IJST/v17i27.1540

Article

Statistical Framework for Modeling Asymmetrical Data with Dual Peaks

VIEWS 22
PDF 5

Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i27.1540

Year: 2024, Volume: 17, Issue: 27, Pages: 2829-2840

Original Article

Statistical Framework for Modeling Asymmetrical Data with Dual Peaks

K M Sakthivel¹, G Vidhya^2∗

¹Professor, Department of Statistics, Bharathiar University, Coimbatore, Tamil Nadu, India
²Research Scholar, Department of Statistics, Bharathiar University, Coimbatore, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:07 May 2024, Accepted Date:24 June 2024, Published Date:16 July 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: To create a comprehensive framework that effectively identifies the most suitable model for asymmetrical data based on its unique characteristics. Methods: This study proposed a new model named Gompertz-Gumbel distribution (GGD) based on the results from the framework which utilizes various statistical tools, as well as information criteria. A dip test is used to check the modality of the data. To propose a new model, the finite mixture model concept was employed. The location, scale, shape, and weight parameters of the GGD were estimated using the maximum likelihood estimation method. Findings: The suggested framework exhibits superior performance in developing a suitable model for the asymmetrical data with dual peaks, resulting in the best fit for the data. To validate the effectiveness of the proposed model, it has been compared with various models like Gaussian models and two-component mixture models. The GGD's properties have also been determined. The various shapes of the GGD were also analyzed. Novelty: A novel framework is proposed to identify the appropriate model for the asymmetrical data with dual peaks that outperform the existing models. It shows the significance of the framework.

Keywords: Lifetime distributions, Mixture models, Information Criteria, Goodness of fit, Asymmetrical data

References

Pearson K. Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society, Series A. 1894;185:71–110. Available from: https://doi.org/10.1098/rsta.1894.0003
Lindley DV. Fiducial distributions and Bayes theorem. Journal of the Royal Statistical Society, Series B. 1958;20(1):102–107. Available from: https://doi.org/10.1111/j.2517-6161.1958.tb00278.x
Sharma V, Shanker R, Shanker R. On some one parameter lifetime distributions and their applications. Annals of Biostatistics & Biometric Applications. 2019;3(2). Available from: http://dx.doi.org/10.33552/ABBA.2019.03.000556
Nwikpe BJ, Cleopas IE. Kpenadidum distribution: statistical properties and application. Asian Journal of Pure and Applied Mathematics. 2022;4(1):759–765. Available from: https://globalpresshub.com/index.php/AJPAM/article/view/1699
Ganaie RA, Rajagopalan V. Exponentiated Aradhana distribution with properties and applications in engineering sciences. Journal of Scientific Research. 2022;6(1):316–325. Available from: http://dx.doi.org/10.37398/JSR.2022.660134
Eyob T, Shanker R, Shukla KK, Leonida TA. Weighted quasi-Akash distribution: properties and applications. American Journal of Mathematics and Statistics. 2019;9(1):30–43. Available from: http://dx.doi.org/10.5923/j.ajms.20190901.05
Aniefiok II, Nwikpe BJ. The Iwok-Nwikpe distribution: statistical properties and application. Asian Journal of Probability and Statistics. 2021;15(1):35–45. Available from: https://doi.org/10.9734/ajpas/2021/v15i130347
Benrabia M, Alzoubi MAL. Alzoubi distribution: properties and applications. Journal of Statistics Applications & Probability- An International Journal. 2022;11(2):625–640. Available from: https://doi.org/10.18576/jsap/110221
Mclachlan G, Lee SX, SR. Finite mixture models. Annual Review of Statistics and Its Application. 2019;6(1):355–378. Available from: https://doi.org/10.1146/annurev-statistics-031017-100325
Pinho GBL, Nobre JS, Cordeiro GM. Continuous probability distributions are generated by the PIPE algorithm. Anais da Academia Brasileira de Ciencias. 2022;94(3). Available from: https://doi.org/10.1590/0001-3765202220201542
Sablica L, Hornik K. mistr: A computational framework for mixture and composite distributions. The R Journal. 2020;12(1):283–299. Available from: https://doi.org/10.32614/rj-2020-003
Shanker R. Rama distribution and its application. International Journal of Statistics and Applications. 2017;7(1):26–35. Available from: http://article.sapub.org/10.5923.j.statistics.20170701.04.html
Shanker R, Sharma S, Shanker U, Shanker R. Janardan distribution and its application to waiting times data. Indian Journal of Applied Research. 2013;3(8):500–502. Available from: https://doi.org/10.15373/2249555x/aug2013/157
Shanker, Sharma S, Shanker U, Shanker R. Sushila distribution and its application to waiting times data. Opinion- International Journal of Business Management. Special Issue on Role of Statistics in Management and Allied Sciences. 2013;3(2):1–11. Available from: https://www.researchgate.net/publication/323265030_SUSHILA_distribution_and_its_application_to_waiting_times_data
Adewusi O, Ogunwale OD, Ayeni TM. Exponential-Gamma distribution. International Journal of Emerging Technology and Advanced Engineering. 2019;9(10):245–249. Available from: https://www.researchgate.net/publication/337008547_Exponential-Gamma_Distribution
Stephens MA. EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association. 1974;69(347):730–737. Available from: https://doi.org/10.2307/2286009
Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control. 1974;19(6):716–723. Available from: https://doi.org/10.1109/TAC.1974.1100705
Wit E, Heuvel EVD, Romeijn JW. 'All models are wrong…’: an introduction to model uncertainty. Statistica Neerlandica. 2012;66(3):217–236. Available from: https://doi.org/10.1111/j.1467-9574.2012.00530.x

Copyright

© 2024 Sakthivel & Vidhya. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)