On the maximum likelihood method for the transmuted exponentiated gamma distribution
The last two decades have seen the development and the popularization of new families of distributions in order to improve data fitting. Because of the complex forms of the probability density functions of these new distributions, the estimation of parameters can only be done by using numerical optimization algorithms but, in many papers, this numerical optimization problem is not studied in depth and the choice of the optimization algorithm is simply neglected. In this paper, we study the disturbing example of the Transmuted exponentiated gamma (TEG) distribution, an important distribution in lifetime tests, for which estimates depend on the selected optimization algorithms. Our aim is to show through the example of the TEG distribution, that, to implement the maximum likelihood method for a distribution, it is necessary to compare several optimization algorithms in order to determine the most effective one before making applications to real data.
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