Função de Intensidade Poisson Perturbada pelo Número de Eventos Recorrentes
DOI:
https://doi.org/10.5540/tema.2013.014.03.0429Abstract
Neste trabalho modela-se a função de intensidade de um processo de Poisson considerando o tempo e o total de recorrências, condicionados ao momento anterior. Adotamos um componente para o processo de Poisson e o outro para o número total de eventos ocorridos nesta mesma unidade. Estudos de simulação e testes de hipóteses empíricos da significância dos parâmetros no modelo foram realizados. A significância dos testes de hipótese de \emph{Wald} e de razão de verossimilhança foi aproximadamente $10\%$ para mais de 50 ocorrências. Um conjunto de dados com tempos de recorrência na aquisição de cosméticos foi modelado adequadamente, tendo parâmetros significativos e valores estimados próximos dos valores observados, justificando a utilização do modelo proposto para tempos e números de recorrências em uma unidade amostral.References
Ascher, H. & Feingold, H. (1984). Reparable Systems Reliability: Modelling, Inference, Misconceptions and Their Causes. New York, Marcel Dekker.
Bain, L. J. & Engelhardt, M. (1980). Inferences on the Parameters and Current System Reliability for a Time Truncated Weibull Process. Technometrics, 22, 421-426.
Cook, R. (1995). The design and analysis of randomized trials with recurrent events. Statistics in Medicine, 14, 2081-2098.
Cook, R. & Lawless, J. (1997). Marginal analysis of recurrent events and a terminating event, Statistics in Medicine, textbf{16}, 911-924.
Cook, R. J. & Lawless, J. F. (2002). Analysis of repeated events. Statistical Methods in Medical Research. 11, 141-166.
Cox, D. R. & Lewis, P. A. W. (1966). The Statistical Analysis of Series of Events. London: Methuen.
Cox, D. R. & Hinkley, D. V. (1974). Theoretical Statistics. London: Chapman & Hall.
Crowder, M. J., Kimber, A. C., Smith, R. L. & Sweeting, T. J. (1991). Statistical Analysis of Reliability Data. London: Chapman and Hall.
Guo, H., Zhao, W. & Mettas, A. (2006). Practical methods for modeling repairable systems with time trends and repair effects. Proceedings of Annual Reliability and Maintainability Symposium, California, 182-188.
Lawless, J. F. (1987). Regression Methods for Poisson Process Data. Journal of the American Statistical Association, 82, 807-815.
Lawless, J.F. & Nadeau, C. (1995). Some simple robust methods for the analysis of recurrent events. Technometrics, 37, 158-168.
Lawless, J. F. & Thiagarajah, K. (1996). A point-process model incorporating renewals and time trends, with application to repairable systems. Technometrics, 38, 131-138.
Lehmann, E. L. (1999). Elements of Large-sample Theory. New York Springer-Verlag, New York.
Lee, L., & Lee, K. (1978). Some Results on Inference for the Weibull Process. Technometrics, 20 41-45. % ok
Lindqvist, B.H., Elvebakk, G. & Heggland K. (2003). The trend-renewal process for statistical analysis of repairable systems. Technometrics, 45, 31-44.
Louzada, F., Mazuchelli, J. & Achcar, J. A. (2002). Introdução à Análise de Sobrevivência e Confiabilidade. III Jornada Regional de Estatística.
Nelson, W. (1995). Confidence Limits for Recurrence Data - Applied to Cost or Number of Product Repair. Technometrics, 37, 147-157.
R Development Core Team (2011). R: A Language and Environment for Statistical Computating. R Foundation for Statistical Computing, Vienna, Austria.
Tomazella, V. L. D. (2003). Modelagem de dados de eventos recorrentes via processos de Poisson com termo de fragilidade, 165p. Tese. (Doutorado em Ciências de Computação e Matemática Computacional)- Instituto de Ciências Matemáticas de São Carlos, Universidade de São Paulo, São Carlos.
Downloads
Additional Files
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.