A New Artificial Intelligence Algorithm to Estimate the Survival Function  of the Modified Log-Logistic Distribution

Mohammed A.R.  Hayoun; Bayda A. Kalaf; Erum  Rehman

doi:10.30526/39.1.4167

Authors

Mohammed A.R. Hayoun Department of Biology, Collage of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Iraq. https://orcid.org/0009-0001-1027-6778
Bayda A. Kalaf Department of Mathematics, College of education for Pure Sciences (ibn Al-Haitham), University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0003-1136-0055
Erum Rehman 3Department of Mathematics, School of Sciences and Humanities (SSH), Nazarbayev University, Astana, Kazakhstan. https://orcid.org/0000-0003-0939-1880

DOI:

https://doi.org/10.30526/39.1.4167

Keywords:

Survival function , particle swarm optimization, gray wolf algorithm, mean square error, simulation

Abstract

Survival analysis is a fundamental statistical tool for studying the period leading up to a specific event, such as patient death or device failure. Interest in this analysis has grown due to its ability to provide accurate insights into survival rates and survival function estimation in various fields. This paper modifies the Log-logistic Distribution ( ) by adding a shape parameter to enhance its ability to predict more effectively. After that, a new hybrid meta-heuristic algorithm (PSWGO), combining particle swarm optimization with the gray wolf algorithm, is proposed to estimate the survival function. To compare and investigate the performance of the proposed algorithm with three meta-heuristic algorithms (particle swarm optimization, the gray wolf algorithm, and genetic algorithm ), and different sample sizes (n = 25, 50, 75, and 100), a simulation study is conducted based on the mean square error (MSE). to obtain the numerical results, MATLAB version 2022a is used. The results showed that the proposed method (PSWGO) provides an accurate and satisfactory estimate for the Survival function, as it has a less mean-square error than the other estimation methods in most cases. MATLAB version 2020a is used to obtain the numerical results

Author Biographies

Mohammed A.R. Hayoun, Department of Biology, Collage of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Iraq.

.
Bayda A. Kalaf, Department of Mathematics, College of education for Pure Sciences (ibn Al-Haitham), University of Baghdad, Baghdad, Iraq

.
Erum Rehman, 3Department of Mathematics, School of Sciences and Humanities (SSH), Nazarbayev University, Astana, Kazakhstan.

.

References

1. In J, Lee DK. Survival analysis: Part II—applied clinical data analysis. Korean J Anesthesiol. 2019;72(5):441–457. https://doi.org/10.4097/kja.19183

2. Akbarinasab M, Arabpour ARM, Abbas M. Truncated log-logistic family of distributions. J Biostat Epidemiol. 2019;5(2):137–47. https://doi.org/10.18502/jbe.v5i2.2345

3. Bidaoui H, El Abbassi I, El Bouardi A, Darcherif A. Wind speed data analysis using Weibull and Rayleigh distribution functions: case study—five cities northern Morocco. Procedia Manuf. 2019;32:786–793. https://doi.org/10.1016/j.promfg.2019.02.286

4. Ibrahim A, Kalaf BA. Estimation of the survival function based on the log-logistic distribution. Int J Nonlinear Anal Appl. 2022;13(1):127–41. https://doi.org/10.22075/ijnaa.2022.5466

5. Ahmed IK, Taha TA, Salman AN. Single stage shrinkage estimation methods for reliability function of generalized exponential distribution using simulation. Iraqi J Sci. 2024:1531–40. https://doi.org/10.24996/ijs.2024.65.3.29

6. Casella G, Berger RL. Statistical Inference. 2nd ed. Boca Raton, FL: CRC Press; 2024. https://doi.org/10.1201/9781003456285

7. Zeng HB, Liu XG, Wang W, Xiao SP. New results on stability analysis of systems with time-varying delays using a generalized free-matrix-based inequality. J Frankl Inst. 2019;356(13):7312–7321. https://doi.org/10.1016/j.jfranklin.2019.03.029. .

8. Gandomi AH, Yang XS, Alavi AH. Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput. 2013;29(1):17–35. https://doi.org/10.1007/s00366-011-0241-y

9. Ali OA. Proposed algorithm for Gumbel distribution estimation. Aust J Basic Appl Sci. 2017;11(16):17–24.

10. Yoon S, Jeong C, Lee T. Application of harmony search to design storm estimation from probability distribution models. J Appl Math. 2013;2013:932943. https://doi.org/10.1155/2013/932943

11. Shin JY, Heo JH, Jeong C, Lee T. Meta-heuristic maximum likelihood parameter estimation of the mixture normal distribution for hydro-meteorological variables. Stoch Environ Res Risk Assess. 2014;28(2):347–58. https://doi.org/10.1007/s00477-013-0753-7

12. Özsoy VS, Örkçü HH. Estimating the parameters of nonlinear regression models through particle swarm optimization. Gazi Univ J Sci. 2016;29(1):187–199.

13. Yang F, Ren H, Hu Z. Maximum likelihood estimation for three-parameter Weibull distribution using evolutionary strategy. Math Probl Eng. 2019;2019:6281781. https://doi.org/10.1155/2019/6281781

14. Yonar A, Yapici N. Evaluation and comparison of metaheuristic methods to estimate the parameters of gamma distribution. Nicel Bilim Derg. 2022;4(1):96–119.

15. Yonar A, Yapici N. A novel differential evolution algorithm approach for estimating the parameters of gamma distribution: an application to the failure stresses of single carbon fibres. Hacet J Math Stat. 2020;49(5):1493–1514.

16. Akbari R, Mohammadi A, Ziarati K. A novel bee swarm optimization algorithm for numerical function optimization. Commun Nonlinear Sci Numer Simul. 2010;15(10):3142–55. https://doi.org/10.1016/j.cnsns.2009.11.003

17. Karaboga D, Basturk B. Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. In: Proc Int Fuzzy Syst Assoc World Congr; 2007. p. 789–798.

18. Kiani F, Seyyedabbasi A, Aliyev R, Gülle M U, Başyıldız H, Shah MH . Adapted-RRT: novel hybrid method to solve three-dimensional path planning problem using sampling and metaheuristic-based algorithms. Neural Comput Appl. 2021;33(22):15569–15599. https://doi.org/10.1007/s00521-021-06179-0

19. Han J, Seo Y. Mobile robot path planning with surrounding point set and path improvement. Appl Soft Comput. 2017;57:35–47. https://doi.org/10.1016/j.asoc.2017.03.035.

20. Bain LJ. Analysis for the linear failure rate life-testing distribution. Technometrics. 1974;16(4):551–559.

21. Ragab A, Green J. On order statistics from the log-logistic distribution and their properties. Commun Stat Theory Methods. 1984;13(21):2713–2724.

22. Kantam RRL, Rosaiah K, Rao GS. Acceptance sampling based on life tests: log-logistic model. J Appl Stat. 2001;28(1):121–128.

23. Kantam RRL, Rao GS, Sriram B. An economic reliability test plan: log-logistic distribution. J Appl Stat. 2006;33(3):291–296.

24. Wolpert DH, Macready WG. No free lunch theorems for optimization. IEEE Trans Evol Comput. 1997;1(1):67–82. https://doi.org/10.1109/4235.585893

25. Mirjalili S, Mirjalili SM, Lewis A. Grey wolf optimizer. Adv Eng Softw. 2014;69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

26. Liu J, Wei X, Huang H. An improved grey wolf optimization algorithm and its application in path planning. IEEE Access. 2021;9:121944–121956. https://doi.org/10.1109/access.2021.3108973