engleski

Parameter estimation for a Three-Parameter Weibull Distribution -A Comparative Study

A large number of models have been derived using the model function of the form of a three-parameter Weibull distribution. In this paper a simulation study which compares three methods for parameter estimation of the three- parameter Weibull distribution using a random sample from that distribution is presented. One of them relies on the maximum likelihood approach ([8]) and the other two are the Weibull probability plot method ([5]) and the weighted least squares method ([3]). The results showed that neither of the applied procedures generally gives the best estimator. It is shown that the maximum likelihood approach has smaller variance than the weighted least squares approach but the procedure which should be used depends on the true value of the shape parameter which is unknown. On the other hand, the least squares approach also gives acceptable estimation and the estimating procedure does not depend on true parameter values. The Weibull probability plot method is computationally the easiest method and it can be used to obtain an initial approximation for numerical computing with the other two approaches. This method also gives excellent results for small values of the shape parameter, i.e. if the density function is strictly decreasing.

three-parameter Weibull distribution ; parameter estimation ; simulation study

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