Implementing particle swarm optimization algorithm to estimate the mixture of two Weibull parameters with censored data

Journal of Statistical Computation and Simulation

Volumn 84, Issue 9, 2014, Pages 1975-1989

  Wang, Fu Kwun ^a   Huang, Ping Ren ^a  

^a NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

Author keywords

maximum likelihood estimation; PSO algorithm; Weibull mixture distributions

Indexed keywords

EID: 84900534639     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949655.2013.778992     Document Type: Article

References (30)

1. Sinha S K. Bayesian estimation of the parameters and reliability function of mixture of Weibull life distributions. J Statist Plann Inference. 1987;16:377-387 doi: 10.1016/0378-3758(87)90090-5
2. Partra K, Dey D K. A multivariate mixture of Weibull distribution in reliability modeling. Statist Probab Lett. 1999;45:225-235 doi: 10.1016/S0167-7152(99)00062-0
3. Kundu D, Basu S. Analysis of incomplete data in presence of competing risks. J Statist Plann Inference. 2000;87:231-239 doi: 10.1016/S0378-3758(99)00193-7
4. Tsionas E G. Bayesain analysis of finite mixtures of Weibull distributions. Comm Statist Theory Methods 2002;31:37-48 doi: 10.1081/STA-120002433
5. Bucar T, Nagode M, Fajdiga M. Reliability approximation using finite Weibull mixture distributions. Reliab Eng Syst Safety. 2004;84:241-151 doi: 10.1016/j.ress.2003.11.008
6. Murthy DN P, Xie M, Jiang R. Weibull models. New York:Wiley; 2004
7. Carta J A, Ramirez P. Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions. Renew Energy. 2007;32:518-531 doi: 10.1016/j.renene.2006.05.005
8. Sultan K S, Ismail M A, Al-Moisheer A S. Mixture of two inverse Weibull distributions: Properties and estimation. Comput Statist Data Anal. 2007;51:5377-5387 doi: 10.1016/j.csda.2006.09.016
9. Mosler K, Scheicher C. Homogeneity testing in a Weibull mixture model. Statist Papers. 2008;49:315-332 doi: 10.1007/s00362-006-0015-6
10. Franco M, Vivo J M. Constraints for generalized mixtures of Weibull distributions with a common shape parameter. Statist Probab Lett. 2009;79:1724-1730 doi: 10.1016/j.spl.2009.05.005
11. Farcomeni A, Nardi A. A two-component Weibull mixture to model early and late mortality in a Bayesian framework. Comput Statist Data Anal. 2010;54:416-428 doi: 10.1016/j.csda.2009.09.007
12. Ebden M, Stranjak A, Roberts S. Visualizing uncertainity in reliability functions with application to aero engine overhaul. J Roy Statist Soc, Ser C. 2010;59:163-173 doi: 10.1111/j.1467-9876.2009.00692.x
13. Mosler K, Haferkamp L. A comparison of recent procedures in Weibull mixture testing. In: Skiadas C H editors. Advances in data analysis. Vol. 5; 2010. p. 211-218
14. Castet J M, Saleh J H. Single versus mixture Weibull distributions for nonparametric satellite reliability. Reliab Eng Syst Safety 2010;95:295-300 doi: 10.1016/j.ress.2009.10.001
15. Franco M, Vivo J M, Balakrishnan N. Reliability properties of generalized mixtures of Weibull distributions with a common shape parameter. J Statist Plann Inference. 2011;141:2600-2613 doi: 10.1016/j.jspi.2011.02.012
16. Dempster A, Laird N, Rubin D. Maximum likelihood from incomplete data via the EM algorithm. J Roy Statist Soc, Ser B. 1977;39:1-38
17. Kennedy J, Eberhart R. Swarm intelligence. San Francisco, CA:Morgan Kaufmann; 2001
18. Kennedy J. Bare bones particle swarms. Proceedings of the IEEE Swarm Intelligence SymposiumIndianapolis, IN; 2003. p. 80-87
19. Campos M, Krohling R A, Borges P. Particle swarm optimization for inference procedures in the generalized Gamma family based on censored data. In: Mehnen J, Köppen M, Saad A, Tiwari A editors. Applications of soft computing. Vol. 58. Berlin, Heidelberg:Springer-Verlag. 2009. p. 411-422
20. Krohling R A, Campos M, Borges P. Bare Bones particle swarm applied to parameter estimation of mixed Weibull distribution. In: Gao X Z, Gaspar-Cunha A, Köppen M, Wang J editors. Soft computing in industrial applications. Vol. 75 Berlin, Heidelberg:Springer-Verlag; 2010. p. 53-60
21. Nelson W. Accelerated testing. New York:Wiley; 1990
22. Kennedy J, Eberhart R. Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks; Perth, Australia; 1995. p. 1941-1948
23. Shi Y, Eberhart R. A modified particle swarm optimizer. In: Proceedings of the IEEE International Conference on Neural Networks; Anchorage, Alaska, USA; 1998. p. 69-73
24. Clerc M, Kennedy J. The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput. 2002;6:58-73 doi: 10.1109/4235.985692
25. Bratton D, Kennedy J. Defining a standard for particle swarm optimization. In: Proceedings of the IEEE Swarm Intelligence Symposium. Honolulu, Hawaii, USA; 2007. p. 120-127
26. Poli R, Kennedy J, Blackwell T. Particle swarm optimization: an overview. Swarm Intell. 2007;1:33-57 doi: 10.1007/s11721-007-0002-0
27. Menon M V. Estimation of the shape and scale parameter of the Weibull distribution. Technometrics 1963;5:175-182 doi: 10.1080/00401706.1963.10490073
28. R Development Core Team. R: a language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2012.
29. Carter AD S. Mechanical reliability. New York:Wiley; 1986
30. Blischke W R, Murthy DN P. Product warranty handbook. New York:Marcel Dekker; 2000