A study of the number of solutions of the system of the log-likelihood equations for the 3-parameter Weibull distribution. (English) Zbl 1263.62034

Tzavelas, George

Appl. Math., Praha 57, No. 5, 531-542 (2012).

In the case of the three parameter Weibull distribution, which plays an important role in life testing and reliability theory, the author considers the system of the log-likelihood equations of the parameters. First, using a solution of the log-likelihood equation on a scale parameter, the shape parameter is derived as a certain form of a function of a location parameter from the log-likelihood equations on a shape and a location parameter. Next, the form of the function of a location parameter and the expression of the form as the location parameter tends to \(-\infty\) are given. Substituting the form into the log-likelihood equation on a shape parameter, the determination of the number of solutions is discussed. Some concrete examples are also given.

Reviewer: Masafumi Akahira (Tsukuba)

MSC:

62F10	Point estimation
62N05	Reliability and life testing

Keywords:

Hessian matrix; maximum likelihood estimator; stationary values

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