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Title: | On the Weibull-Gamma frailty model, its infinite moments, and its connection to generalized log-logistic, logistic, Cauchy, and extreme-value distributions | Authors: | MOLENBERGHS, Geert VERBEKE, Geert |
Issue Date: | 2011 | Publisher: | ELSEVIER SCIENCE BV | Source: | JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 141 (2). p. 861-868 | Abstract: | It is shown that the commonly used Weibull-Gamma frailty model has a finite number of finite moments only and that its marginal distribution generalizes the log-logistic distribution. In some cases there is not even a finite variance, and there are cases without a single finite moment. Upon transformation to the entire real line, generalized logistic and generalized Cauchy distributions are introduced and their connection with the previous ones established, as well as with the extreme-value distribution. Apart from intrinsic and classroom value, the family can be of use when formulating non-informative priors in Bayesian data analysis. Also, gauging the amount of finite moments is important when checking regularity conditions in the Weibull-Gamma model. Our findings are illustrated using data from survival in cancer patients. (c) 2010 Elsevier B.B. All rights reserved. | Notes: | [Molenberghs, Geert; Verbeke, Geert] Univ Hasselt, Interuniv Inst Biostat & Stat Bioinformat, B-3590 Diepenbeek, Belgium. [Molenberghs, Geert; Verbeke, Geert] Katholieke Univ Leuven, Interuniv Inst Biostat & Stat Bioinformat, B-3000 Leuven, Belgium. geert.molenberghs@uhasselt.be | Keywords: | Cauchy distribution; Exponential frailty; Gamma frailty; Weibull model;cauchy distribution; exponential frailty; gamma frailty; Weibull model | Document URI: | http://hdl.handle.net/1942/11400 | Link to publication/dataset: | http://scinet.dost.gov.ph/union/ShowSearchResult.php?s=2&f=&p=&x=&page=&sid=1&id=On+the+Weibull-Gamma+frailty+model%2C+its+infinite+moments%2C+and+its+connection+to+generalized+log-logistic%2C+logistic%2C+Cauchy%2C+and+extreme-value+distributions&Mtype=NONPRINTS | ISSN: | 0378-3758 | e-ISSN: | 1873-1171 | DOI: | 10.1016/j.jspi.2010.08.008 | ISI #: | 000284386500025 | Rights: | (c) 2010 Elsevier B.V. All rights reserved | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2011 |
Appears in Collections: | Research publications |
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