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**Finding maximum likelihood estimators for the three-parameter Weibull distribution.**
*(English)*
Zbl 0807.62021

Summary: Much work has been devoted to the problem of finding maximum likelihood estimators for the three-parameter Weibull distribution. This problem has not been clearly recognized as a global optimization one and most methods from the literature occasionally fail to find a global optimum. We develop a global optimization algorithm which uses first order conditions and projection to reduce the problem to a univariate optimization one. Bounds on the resulting function and its first order derivative are obtained and used in a branch-and-bound scheme. Computational experience is reported. It is also shown that the solution method we propose can be extended to the case of right censored samples.

### MSC:

62F10 | Point estimation |

90C90 | Applications of mathematical programming |

90C30 | Nonlinear programming |

65C99 | Probabilistic methods, stochastic differential equations |

### Keywords:

bounds; decomposition; maximum likelihood estimators; three-parameter Weibull distribution; global optimization algorithm; first order conditions; projection; univariate optimization; first order derivative; branch-and-bound scheme; right censored samples
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\textit{É. Gourdin} et al., J. Glob. Optim. 5, No. 4, 373--397 (1994; Zbl 0807.62021)

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### References:

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