ALIENOR METHOD APPLIED IN STATISTICS: OPTIMIZATION OF KATZ’S AND COM-POISSON’S LIKELIHOOD FUNCTIONS

A BSTRACT . In this paper, we are interested in a new approach to optimizing the likelihood function of a distribution using the Alienor method. Indeed, the Alienor method is an optimization technique that allows to reduce a multivariate optimization problem to a single variable optimization problem that is easy to solve numerically. For this purpose, we consider the Katz and COM-Poisson distributions, whose maximization of their likelihood functions requires numerical methods. In a first step, we used real data, and, in a second step, we performed a simulation study. The results obtained are satisfactory, and the Alienor method proves to be very interesting in statistics, both for its simplicity and for its performance in converging to the absolute optimum.