Abstract
The generalized gamma distribution offers a highly flexible family of models for lifetime data and includes a considerable number of distributions as special cases. This work deals with the use of the particle swarm optimization (PSO) algorithm in the maximum likelihood estimation of distributions of the generalized gamma family (GG-family) based on data with censored observations.We also discuss a procedure for testing whether a distribution that belong to GG-family is appropriate for lifetime data using the generalized likelihood ratio test principle. Finally, we present two illustrative applications using real data sets. For each data set, we use the PSO algorithm to fit several distributions of the GG-family simultaneously. Then, we test the appropriateness of each fitted model and select the most appropriate one using the Bayesian information criterion or the Akaike information criterion.
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References
Stacy, E.: A generalization of the gamma distribution. Annals of Mathematical Statistics 33, 1187–1192 (1962)
Johnson, N., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions, 2nd edn., vol. 1. John Wiley and Sons, New York (1994)
Stacy, E., Mihram, G.: Parameter estimation for a generalized gamma distribution. Technometrics 7, 349–358 (1965)
Hagar, H., Bain, L.: Inferential procedures for the generalized gamma distribution. Journal of the American Statistical Association 65, 1601–1609 (1970)
Prentice, R.: A log gamma model and its maximum likelihood estimation. Biometrika 61, 539–544 (1974)
Lawless, J.: Inference in the generalized gamma and log gamma distributions. Technometrics 22, 409–419 (1980)
Lawless, J.: Statistical Models and Methods for Lifetime Data. John Wiley and Sons, New York (1982)
Di Ciccio, T.: Approximate inference for the generalized gamma distribution. Technometrics, 33–40 (1987)
Phan, T., Almhana, J.: The generalized gamma distribution: its hazard rate and stress-strength model. IEEE Transactions on Reliability 44, 392–397 (1995)
Dadpay, A., Soofi, E., Soyer, R.: Information measures for generalized gamma family. Journal of Econometrics 56, 568–585 (2007)
Yacoub, M.: The α-μ distribution: a physical fading model for the Stacy distribution. IEEE Transactions on Vehicular Technology 56, 27–34 (2007)
Khuri, A.: Advanced Calculus with Applications, 2nd edn. John Wiley and Sons, New York (2003)
Garthwaite, P., Jolliffe, I., Jones, B.: Statistical Inference, 2nd edn. Oxford University Press, New York (2002)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 1941–1948. IEEE Service Center, Piscataway (1995)
Kennedy, J., Eberhart, R., Shi, Y.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)
Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Second International Symposium on Information Theory, pp. 267–281 (1973)
Schwarz, G.: Estimating the dimension of a model. Annals of Statistics 6, 461–464 (1978)
Clerc, M., Kennedy, J.: The particle swarm - explosion, stability, and convergence in a with multidimensional complex space. IEEE Transactions on Evolutionary Computation 6, 58–73 (2002)
Dai, Y., Zhou, Y.-F., Jia, Y.-Z.: Distribution of time between failures of machining center based on type I censored data. Reliability Engineering and System Safety 79, 377–379 (2003)
Wilk, M., Gnanadesikan, R., Huyett, M.: Estimation of parameters of the gamma distribution using order statistics. Biometrika 49, 525–545 (1962)
Kaplan, E., Meier, P.: Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53, 457–481 (1958)
Clerc, M.: Particle Swarm Optimization. ISTE Publishing Company, London (2006)
Kennedy, J., Mendes, R.: Neighborhood topologies in fully informed and best-of-neighborhood particle swarms. IEEE Transactions on Systems, Man and Cybernetic 36, 515–519 (2006)
Krohling, R., Coelho, L.: Coevolutionary particle swarm optimization using gaussian distribution for solving constrained optimization problems. IEEE Transactions on Systems, Man and Cybernetics 36, 1407–1416 (2006)
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Campos, M., Krohling, R.A., Borges, P. (2009). Particle Swarm Optimization for Inference Procedures in the Generalized Gamma Family Based on Censored Data. In: Mehnen, J., Köppen, M., Saad, A., Tiwari, A. (eds) Applications of Soft Computing. Advances in Intelligent and Soft Computing, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89619-7_40
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DOI: https://doi.org/10.1007/978-3-540-89619-7_40
Publisher Name: Springer, Berlin, Heidelberg
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