A note on multiple roots of a likelihood equation for Weibull sequential order statistics

Marcus Johnen (), Stefan Bedbur and Udo Kamps
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Marcus Johnen: RWTH Aachen University
Stefan Bedbur: RWTH Aachen University
Udo Kamps: RWTH Aachen University

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 4, No 6, 519-525

Abstract: Abstract A multi-sample set-up of sequential order statistics from Weibull distribution functions with known scale parameters and a common unknown shape parameter is considered. The respective likelihood equation may have multiple roots even in the single-sample case, which is demonstrated by a simple example and illustrated with a simulation study. Uniqueness of the root of the likelihood equation and of the maximum likelihood estimator is examined with respect to different models of ordered data, sufficient conditions for uniqueness are shown, and the distribution of the number of roots of the likelihood equation is seen to be independent of the unknown shape parameter.

Keywords: Common shape parameter; Maximum likelihood estimation; Order statistics; Weibull distribution (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00184-019-00743-4

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