COMPARISON OF THE USE OF BIO-INSPIRED ALGORITHMS AND CONVENTIONAL METHODS FOR ESTIMATING THE POWER FACTOR IN TWEEDY DISTRIBUTIONS
Keywords:
Tweedy distribution, parameter estimation, heuristic meta-optimization, maximum likelihood, profile likelihood, MoM, MLE, Bayesian methodsAbstract
This paper will estimate the parameters of Tweedie distribution and make use of both the traditional methods and nature-inspired optimization algorithms to estimate the distribution through realistic rainfall data in Kirkuk, Iraq. These estimation methods were the method of moments (MoM), Bayesian method, maximum likelihood (MLE), and profile likelihood, and evolutionary algorithms, namely, the genetic algorithm (GA), molecular swarm algorithm (PSO), gray wolf algorithm (GWO), and white whale algorithm (WOA) . Different indices of trade-offs (maximum likelihood (MLE) method, PSO and GA algorithms) were used to assess the performance of various models; it was found that these algorithms give better results in terms of goodness of fit (AIC and BIC) and predictive accuracy (RMSE and MAE). Conversely, the moment method showed low performance as compared to other methods though the GWO and WOA algorithm gave acceptable and less stable estimates. In addition, the partial likelihood approach was also found to be sensitive to network settings, which produced unreliable results. The Bayesian model offered a convenient probabilistic method of parameters distributions, yet it needs additional software enhancement to address the Tweedy distribution better. The paper found the maximum likelihood approach (MLE) and the most recent optimization techniques, including PSO and GA, to be the best options to easily and precisely estimate Tweedy distribution parameters. The research suggests that more sophisticated optimization methods should be used and more specific Bayesian applications should be created to assist the investigation of such distribution in the upcoming studies.
References
S. D. Temple and C. Sinclair, “The Tweedie Index Parameter and Its Estimator An Introduction with Applications to Actuarial Ratemaking Title: The Tweedie Index Parameter and Its Estimator: An Introduction with Applications to Actuarial Ratemaking Approved,” no. June, 2018.
A. Ghribi, A. Hassin, and A. Masmoudi, “on the Existence of the Tweedie Power Parameter Implicit Estimator,” Bull. Korean Math. Soc., vol. 59, no. 4, pp. 979–991, 2022, doi: 10.4134/BKMS.b210590.
T. Swan, “Generalized estimating equations when the response variable has a Tweedie distribution: an application for multi-site rainfall modelling,” Dissertation, p. 168, 2006, [Online]. Available: http://eprints.usq.edu.au/3388
W. H. Bonat and C. C. Kokonendji, “Flexible Tweedie regression models for continuous data,” J. Stat. Comput. Simul., vol. 87, no. 11, pp. 2138–2152, 2017, doi: 10.1080/00949655.2017.1318876.
P. K. Dunn and G. K. Smyth., “Series evaluations of Tweedie exponen- tial dispersion models.,” Stat. Comput. Accept. Publ., 2005.
P. Dunn. and Tweedie:, “Tweedie exponential fam- ily models.,” R Packag. http//www.sci.usq.edu.au/staff/dunn/twhtml/home.html, vol. version 1., 2004.
S. G. Candy, “Modelling catch and effort data using generalized linear models, the Tweedie distribution, random vessel effects and random stratum-by-year effects.,” CCAMLR Sci. Davis, vol. 11, pp. 59–80, 2004.
M. Tweedie, “An index which distinguishes between some important exponential families,”,” pp. 579-604 2 wood, 1984.
B. Jørgensen, “The theory of exponential dispersion models and analysis of deviance,” 1992.
W. A. Hadba, “Tweedie regularization model and application,” Commun. Stat. - Theory Methods, vol. 54, no. 6, pp. 1729–1746, 2025, doi: 10.1080/03610926.2024.2349698.
M. H. Ndegwa, “CLAIM RESERVING USING TWEEDIE DISTRIBUTION School of Mathematics University of Nairobi,” no. July, 2013.
B. Jørgensen., “Exponential dispersion models (with discussion).,” Jour- nal R. Stat. Soc. Ser. B Stat. Methodol., vol. 49, pp. 127–162, 1987.
babakr Sawen Othman. & Badal Mohammed AbdulMajeed., “Using Multilevel Poisson Regression with Wavelets Filters.,” Univ. Kirkuk J. Adm. Econ. Sci., vol. 13, no. 4, pp. 179–192, 2023.
Abduljabbar Luay Adil., “Ridge-Type Estimator for the Poisson-inverse Gaussian regression model.,” Univ. Kirkuk J. Adm. Econ. Sci., vol. 15, no. 2, pp. 405–413, 2025.
P. K. Dunn and G. K. Smyth., “Randomized quantile residuals.,” J. Comput. Graph. Stat., vol. 5, pp. 1–10, 1996.
P. K. Dunn and G. K. Smyth, Evaluation of Tweedie exponential dispersion model densities by Fourier inversion, vol. 18, no. 1. 2008. doi: 10.1007/s11222-007-9039-6.
Peter Dunn., “Package ’tweedie’. R Documentation.,” Packag. R Program. Dec., 2016.
P. K. Dunn and G. K. Smyth, “Series evaluation of Tweedie exponential dispersion model densities,” Stat. Comput., vol. 15, no. 4, pp. 267–280, 2005, doi: 10.1007/s11222-005-4070-y.
D. B. Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D., Vehtari, A., & Rubin, “Bayesian Data Analysis,” (3rd ed.). CRC Press.
A. J. Dobson and A. G. Barnett, An introduction to generalized linear models, third edition. 2008. doi: 10.1080/02664760802695900.
Z. Wu, X. Duan, and W. Zhang, “Bayesian Analysis of Tweedie Compound Poisson Partial Linear Mixed Models with Nonignorable Missing Response and Covariates,” Entropy, vol. 25, no. 3, 2023, doi: 10.3390/e25030506.
Puguh Jayadi, Khairul Adilah binti Ahmad, Rayhan Zulfitri Dwi Cahyo, and Jofanza Denis Aldida, “Particle Swarm Optimization-based Linear Regression for Software Effort Estimation,” J. Inf. Syst. Technol. Eng., vol. 2, no. 2, pp. 261–268, 2024, doi: 10.61487/jiste.v2i2.69.
H.-I. Hsieh, T.-P. Lee, and T.-S. Lee, “A Hybrid Particle Swarm Optimization and Support Vector Regression Model for Financial Time Series Forecasting,” Int. J. Bus. Adm., vol. 2, no. 2, pp. 48–56, 2011, doi: 10.5430/ijba.v2n2p48.
Y. (2001b). Eberhart, R. C., & Shi, “Particle Swarm Optimization: Developments, Applications and Resources.,” Proc. Congr. Evol. Comput. , IEEE Serv. Center, Seoul, pp. 81–86, 2001.
G. Wolf and O. Gwo, “Chapter 9 Grey Wolf Optimization ( GWO ) Algorithm,” no. July, 2018, doi: 10.1007/978-981-10-5221-7.
A. Mirjalili, S., Mirjalili, S. M., & Lewis, “Grey Wolf Optimizer. Advances in Engineering Software,” vol. 69, pp. 46–6.
S. Gholizadeh, “Optimal design of double layer grids considering nonlinear behaviour by sequential grey wolf algorithm.,” J. Optim. Civ. Eng., vol. 5, no. 4, pp. 511–523, 2015.
R. Muro, C., Escobedo, R., Spector, L., & Coppinger, “Wolf-pack (Canis Lupus) hunting strategies emerge from simple rules in computational simulations.,” Behav. Process., vol. 88, no. 3, pp. 192–197, 2011.
S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Adv. Eng. Softw., vol. 69, pp. 46–61, 2014.
D. Perin, A. D. Karaoglan, and K. Yilmaz, “Using grey wolf optimizer to minimize voltage total harmonic distortion of a salient-pole synchronous generator,” Sci. Iran., vol. 30, no. 2 D, pp. 592–604, 2023, doi: 10.24200/sci.2021.57657.5349.
A. Goli, H. K. Zare, R. Tavakkoli-Moghaddam, and A. Sadeghieh, “An Improved Artificial Intelligence Based on Gray Wolf Optimization and Cultural Algorithm to Predict Demand for Dairy Products: A Case Study,” Int. J. Interact. Multimed. Artif. Intell., vol. 5, no. 6, pp. 15–22, 2019, doi: 10.9781/ijimai.2019.03.003.
R. Sihwail, M. Al Ghamri, and D. Ibrahim, “An Enhanced Model of Whale Optimization Algorithm and K-nearest Neighbors for Malware Detection,” Int. J. Intell. Eng. Syst., vol. 17, no. 3, pp. 606–621, 2024, doi: 10.22266/ijies2024.0630.47.
M. H. Nadimi-Shahraki, H. Zamani, Z. Asghari Varzaneh, and S. Mirjalili, “A Systematic Review of the Whale Optimization Algorithm: Theoretical Foundation, Improvements, and Hybridizations,” Arch. Comput. Methods Eng., pp. 1–47, 2023.
N. Khodadadi, E. S. M. El-kenawy, S. Faridmarandi, M. S. Ghahfarokhi, A. Ibrahim, and S. Mirjalili, “A novel version of whale optimization algorithm for solving optimization problems,” Handb. Whale Optim. Algorithm Var. Hybrids, Improv. Appl., no. November, pp. 591–600, 2023, doi: 10.1016/B978-0-32-395365-8.00048-8.
D. E. ( Goldberg, “Genetic Algorithms in Search, Optimization, and Machine Learning.,” Addison-Wesley., 1989.
M. A. Iquebal, Prajneshu, and H. Ghosh, “Genetic algorithm optimization technique for linear regression models with heteroscedastic errors,” Indian J. Agric. Sci., vol. 82, no. 5, pp. 422–425, 2012, doi: 10.56093/ijas.v82i5.17802.
Z. Y. Algamal and H. M.Thabet, “Using Genetic Algorithm in Outlier Detection for Regression Model,” J. Educ. Sci., vol. 27, no. 3, pp. 136–142, 2018, doi: 10.33899/edusj.2018.159314.
S. Paterlini and T. Minerva, “Regression model selection using genetic algorithms,” Proc. 11th WSEAS Int. Conf. Neural Networks, NN ’10, Proc. 11th WSEAS Int. Conf. Evol. Comput. EC ’10, Proc. 11th WSEAS Int. Conf. Fuzzy Syst. FS ’10, no. January 2010, pp. 19–27, 2010.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
CC BY
This license enables reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use. CC BY includes the following elements:
BY: credit must be given to the creator.
