  The paper is devoted to the study of a parametric deformation model of
independent and identically random variables. Firstly, we construct an
efficient and very easy to compute recursive estimate of the parameter. Our
stochastic estimator is similar to the Robbins-Monro procedure where the
contrast function is the Wasserstein distance. Secondly, we propose a recursive
estimator similar to that of Parzen-Rosenblatt kernel density estimator in
order to estimate the density of the random variables. This estimate takes into
account the previous estimation of the parameter of the model. Finally, we
illustrate the performance of our estimation procedure on simulations for the
Box-Cox transformation and the arcsinh transformation.
