A Note on Local Maxima in Quadratic Transmuted Distributions Likelihoods

Transmutation is a widely used technique for generalizing probability distributions to improve data fitting. Its implementation often relies on maximum likelihood estimation, which reduces to a box-constrained numerical optimization problem. Despite this, many studies overlook the crucial role of the initial values required to start the optimization algorithm. In this paper, we demonstrate through two case studies on real data that improper parameter initialization can lead to convergence toward local maxima, ultimately resulting in biased estimates and incorrect conclusions. We show that the choice of starting values can significantly affect both the convergence behavior and the reliability of the final results. This study highlights the need for greater methodological rigor and increased awareness regarding parameter initialization in iterative estimation procedures, particularly within the context of transmuted distributions in order to avoid erroneous conclusions.