  The study of accurate methods to estimate the distribution of stellar
rotational velocities is important for understanding many aspects of stellar
evolution. From such observations we obtain the projected rotational speed v
sin(i) in order to recover the true distribution of the rotational velocity. To
that end, we need to solve a difficult inverse problem that can be posed as a
Fredholm integral of the first kind. n this work we have used a novel approach
based on Maximum likelihood (ML) estimation to obtain an approximation of the
true rotational velocity probability density function expressed as a sum of
known distribution families. In our proposal, the measurements have been
treated as random variables drawn from the projected rotational velocity
probability density function. We analyzed the case of Maxwellian sum
approximation, where we estimated the parameters that define the sum of
distributions. The performance of the proposed method is analyzed using Monte
Carlo simulations considering two theoretical cases for the probability density
function of the true rotational stellar velocities: i) an unimodal Maxwellian
probability density distribution and ii) a bimodal Maxwellian probability
density distribution. The results show that the proposed method yielded more
accurate estimates in comparison with the Tikhonov regularization method,
especially for small sample length N=50. Our proposal was evaluated using real
data from three sets of measurements, and our findings were validated using
three statistical tests. The ML approach with Maxwellian sum approximation is a
accurate method to deconvolve the rotational velocity probability density
function, even when the sample length is small (N= 50)
