Geodesic
A study of the number of solutions of the system of the log-likelihood equations for the 3-parameter Weibull distribution
Applications of Mathematics, Tome 57 (2012) no. 5, pp. 531-542.

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The maximum likelihood estimators of the parameters for the 3-parameter Weibull distribution do not always exist. Furthermore, computationally it is difficult to find all the solutions. Thus, the case of missing some solutions and among them the maximum likelihood estimators cannot be excluded. In this paper we provide a simple rule with help of which we are able to know if the system of the log-likelihood equations has even or odd number of solutions. It is a useful tool for the detection of all the solutions of the system.
DOI : 10.1007/s10492-012-0031-x
Classification : 62F10, 62F99, 62N05
Keywords: Weibull distribution; Hessian matrix; maximum likelihood estimator; stationary value 
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     title = {A study of the number of solutions of the system of the log-likelihood equations for the 3-parameter {Weibull} distribution},
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Tzavelas, George. A study of the number of solutions of the system of the log-likelihood equations for the 3-parameter Weibull distribution. Applications of Mathematics, Tome 57 (2012) no. 5, pp. 531-542. doi : 10.1007/s10492-012-0031-x. http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0031-x/

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