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Activity Number:
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314
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Type:
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Contributed
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Date/Time:
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Wednesday, August 11, 2004 : 9:00 AM to 10:50 AM
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Sponsor:
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Section on Physical and Engineering Sciences
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| Abstract - #300705 |
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Title:
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Model Reduction of a Three-parameter Model for Survival Distributions to Two-parameter Weibull and Generalized Exponential Models in Estimation of Small Quantiles
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Author(s):
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Elliott Nebenzahl*+ and Dean H. Fearn
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Companies:
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California State University, Hayward and California State University, Hayward
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Address:
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25800 Carlos Bee Boulevard, Hayward, CA, 94542-3435,
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Keywords:
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survival distributions ; parametric models ; model reduction
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Abstract:
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The exponentiated Weibull (EW) distribution depends on three parameters: a scale parameter and two other parameters that affect its shape. Special cases are the Weibull (W) distribution where one of the shape parameters is equal to 1 and the generalized exponential (GE) which has the other shape parameter equal to 1. We are interested in the performance of the GE and W estimates of the EW quantile and in a comparison of the two, in terms of which one more accurately estimates the true EW quantile. If reasonable estimates of the true quantile can be found, then we can operate with the simpler two-parameter models (Weibull and generalized exponential) rather than the more complicated tree-parameter EW model. We check whether either of the two-parameter models are satisfactory by considering, for a large sample of EW data, the ratio of the GE fit of a quantile to the EW fit of the quantile along with the ratio of the W fit of the quantile to the EW fit. For small values of the quantile we give ranges of the values of the shape parameters of the EW distribution that allow a satisfactory GE and/or W fit.
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