The Expectation-Maximization (EM) Algorithm is a widely used method allowing to estimate the maximum likelihood of models involving latent variables. When the Expectation step cannot be computed easily, one can use stochastic versions of the classical EM such as the Stochastic Approximation EM (SAEM). This algorithm, however, has the disadvantage to require the joint likelihood to belong to the curved exponential family. This hypothesis is a bottleneck in a lot of practical situations where it is not verified. To overcome this problem, Kuhn and Lavielle (2005) introduce a rewriting of the model which ``exponentializes'' it. It consists in considering the parameter as an additional latent variable following a Normal distribution centered on the newly defined parameters and with fixed variance. The likelihood of this new exponentialized model now belongs to the curved exponential family and stochastic EM algorithms apply. Although often used, there is no guarantee that the estimated mean will be close to the maximum likelihood estimate of the initial model. In this paper, we will quantify the error done in this estimation while considering the exponentialized model instead of the initial one. More precisely, we will show that this error tends to 0 as the variance of the new Gaussian distribution goes to 0 while computing an upper bound. By verifying those results on an example, we will see that a compromise must be made in the choice of the variance between the speed of convergence and the tolerated error. Finally, we will propose a new algorithm allowing a better estimation of the parameter in a reasonable computation time.