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Extended Burr XII regression models: theory and applications.(English)Zbl 1342.62169

Summary: We introduce two new lifetime distributions by compounding the Burr XII (BXII) and geometric distributions. We derive their moments and moment-generating and quantile functions. We also define two new extended regression models based on the logarithms of these distributions. The regression models are very useful in the analysis of real data since they can provide better fits than other special regression models. We formulate a new cure rate survival model, where the number of competing causes of the event of interest follows a geometric distribution and the time to this event has the BXII geometric distribution. The estimation of the model parameters is performed by maximum likelihood. We illustrate the importance of the new models by means of two real datasets. The first dataset comes from a study carried out at the Department of Entomology of the Luiz de Queiroz School of Agriculture, University of São Paulo, which aims to assess the longevity of the Mediterranean fruit fly (ceratitis capitata). The second dataset comes from the area of biology.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62E10 Characterization and structure theory of statistical distributions
62N05 Reliability and life testing

Software:

Ox;timereg

Cite

References:

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[19]Ortega, E.M.M., Cordeiro, G.M. and Pascoa, M.A.R. (2011). The Generalized Gamma Geometric Distribution. Journal of Statistical Theory and Applications,10, 433-454.
[20]Parker, S. L., Tong, T., Bolden, S. and Wingo, P. (1996). Cancer Statistics, CA A Cancer. Journal for Clinicians, 46, 5-27. ·doi:10.3322/canjclin.46.1.5
[21]Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I. (1986). Integrals and Series, vol. 1. Gordon and Breach Science Publishers, Amsterdam. ·Zbl 0606.33001
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[24]Silva, G.O., Ortega, E.M.M., Garibay, V.C. and Barreto, M.L. (2008). Log-Burr XII regression models with censored Data. Computational Statistics and Data Analysis,52, 3820-3842. ·Zbl 1452.62847 ·doi:10.1016/j.csda.2008.01.003
[25]Silva, G.O., Ortega, E.M.M. and Paula, G.A. (2011). Residuals for Log-Burr XII Regression Models in Survival Analysis. Journal of Applied Statistics,38, 1435-1445. ·Zbl 1218.62103 ·doi:10.1080/02664763.2010.505950
[26]Silva, M.A., Bezerra-Silva, G.C.D., Vendramim, J.D. and Mastrangelo, T. (2013). Sublethal effect of neem extract on Mediterranean fruit fly adults. Revista Brasileira de Fruticultura,35, 93-101. ·doi:10.1590/S0100-29452013000100012
[27]Tsodikov, A.D., Ibrahim, J.G. and Yakovlev, A.Y. (2003). Estimating cure rates from survival data: an alternative to two-component mixture models. Journal of the American Statistical Association, 98, 1063-1078. ·doi:10.1198/01622145030000001007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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