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The study of accurate methods to estimate the distribution of stellarrotational velocities is important for understanding many aspects of stellarevolution. From such observations we obtain the projected rotational speed vsin(i) in order to recover the true distribution of the rotational velocity. Tothat end, we need to solve a difficult inverse problem that can be posed as aFredholm integral of the first kind. n this work we have used a novel approachbased on Maximum likelihood (ML) estimation to obtain an approximation of thetrue rotational velocity probability density function expressed as a sum ofknown distribution families. In our proposal, the measurements have beentreated as random variables drawn from the projected rotational velocityprobability density function. We analyzed the case of Maxwellian sumapproximation, where we estimated the parameters that define the sum ofdistributions. The performance of the proposed method is analyzed using MonteCarlo simulations considering two theoretical cases for the probability densityfunction of the true rotational stellar velocities: i) an unimodal Maxwellianprobability density distribution and ii) a bimodal Maxwellian probabilitydensity distribution. The results show that the proposed method yielded moreaccurate estimates in comparison with the Tikhonov regularization method,especially for small sample length N=50. Our proposal was evaluated using realdata from three sets of measurements, and our findings were validated usingthree statistical tests. The ML approach with Maxwellian sum approximation is aaccurate method to deconvolve the rotational velocity probability densityfunction, even when the sample length is small (N= 50)

astronomy and astrophysics

A method to deconvolve stellar rotational velocities III. The  probability distribution function via Maximum Likelihood utilizing Finite  Distribution Mixtures