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                Department of Mathematical Sciences                       
                   The Johns Hopkins University                           
                                                                        
                              SEMINAR                                
                                                                        
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Professor Olga I. Cordero-Brana                   April 6, 2000
Mathematics and Statistics Department             304 Whitehead Hall
American University                               Preseminar: 3:00 p.m.
(visiting Deptartment of Mathematics,             Refreshments: 3:30 p.m.
  Arizona State University)                       Seminar: 4:00 p.m.

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     ESTIMATION OF FAILURE TIMES INVOLVING WEIBULL DISTRIBUTIONS
                      VIA STOCHASTIC ALGORITHMS

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                             ABSTRACT

The Weibull distribution is one of the most frequently employed
distributions for modeling failure time situations.  It is used to describe
simple failure times arising from a single distribution, competing risk
models where the distribution of interest is the poly-Weibull distribution
(infimum of Weibull failure times), and finite mixture models.  In many
circumstances, the maximum likelihood (ML) approach provides satisfactory
estimates of the shape and scale parameters of a Weibull distribution and
can be regarded as a reference technique.

However, ML estimation turns out to be imprecise or even unreliable for
small or highly censored samples.  The behavior of standard ML inference is
worse for estimating poly-Weibull distributions or mixtures of Weibull
distributions.

In this talk, we show that several stochastic algorithms, taking advantage
of the incomplete data structure of the above-mentioned problems, provide
reliable parameter estimates.  We also discuss the rationale for such
satisfactory behavior.

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