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We propose a new approach for estimating the parameters of a probabilitydistribution. It consists on combining two new methods of estimation. The firstis based on the definition of a new distance measuring the difference betweenvariations of two distributions on a finite number of points from their supportand on using this measure for estimation purposes by the method of minimumdistance. For the second method, given an empirical discrete distribution, webuild up an auxiliary discrete theoretical distribution having the same supportof the first and depending on the same parameters of the parent distribution ofthe data from which the empirical distribution emanated. We estimate then theparameters from the empirical distribution by the usual statistical methods. Inpractice, we propose to compute the two estimations, the second based onmaximum likelihood principle of known theoretical properties, and the firstbeing as a control of the effectiveness of the obtained estimation, and forwhich we prove the convergence in probability, so we have also a criterion onthe quality of the information contained in the observations. We apply theapproach to truncated or grouped and censored data situations to give theflavour on the effectiveness of the approach. We give also some interestingperspectives of the approach including model selection from truncated data,estimation of the initial trial value in the celebrate EM algorithm in the caseof truncation and merged normal populations, a test of goodness of fit based onthe new distance, quality of estimations and data.

A New Approach of Point Estimation from Truncated or Grouped and Censored Data